How to calculate the volume of a cylinder in m3 formula. How to find volume in cubic meters

One of the most interesting problems of geometry, the result of which is important in physics, chemistry, and other areas, is the determination of volumes. Doing math at school, children often ask themselves the thought: “Why do we need this?” The world around seems so simple and clear that certain school knowledge is classified as "unnecessary". But it is necessary to face, for example, transportation and the question arises of how to calculate the volume of cargo. You say that there is nothing easier? You are wrong. Knowledge of calculation formulas, the concepts of "substance density", "bulk density of bodies" become necessary.

School knowledge - practical basis

School teachers, teaching the basics of geometry, offer us the following definition of volume: the part of the space occupied by the body. At the same time, the formulas for determining volumes have long been written down, and you can find them in reference books. Mankind learned to determine the volume of a body of the correct form long before the appearance of the treatises of Archimedes. But only this great Greek thinker introduced a technique that makes it possible to determine the volume of any figure. His conclusions became the basis of integral calculus. Volumetric figures are considered to be obtained in the process of rotating flat

Euclidean geometry with a certain accuracy allows you to determine the volume:

The difference between flat and volumetric figures does not allow answering the question of some sufferers about how to calculate the volume of a rectangle. It's about the same as finding something, I don't know what. Confusion in the geometric material is possible, while a rectangle is sometimes called a cuboid.

What to do if the shape of the body is not so well defined?

Determining the volume of complex geometric structures is not an easy job. It is necessary to be guided by several unshakable principles.

• Any body can be broken down into simpler parts. The volume is equal to the sum of the volumes of its individual parts.
• Equal-sized bodies have equal volumes, the parallel transfer of bodies does not change its volume.
• The unit of volume is the volume of a cube with an edge of unit length.

The presence of irregularly shaped bodies (remember the notorious crown of King Heron) does not become a problem. Determining the volumes of bodies is quite possible. This is the process of directly measuring the volumes of a liquid with a body immersed in it, which will be discussed below.

Various applications for volume determination

Let's return to the problem: how to calculate the volume of transported goods. What is the cargo: packaged or bulk? What are the container parameters? There are more questions than answers. The issue of the mass of the cargo will become important, since the transport differs in carrying capacity, and the routes - in the maximum weight of the vehicle. Violation of the rules of transportation threatens with penalties.

Task 1. Let the cargo be rectangular containers filled with goods. Knowing the weight of the goods and the container, you can easily determine the total weight. The volume of the container is defined as the volume of a rectangular parallelepiped.

Knowing the carrying capacity of the transport, its dimensions, it is possible to calculate the possible volume of the transported cargo. The correct ratio of these parameters allows you to avoid a catastrophe, premature failure of transport.

Task 2. Cargo - bulk material: sand, crushed stone and the like. At this stage, only a great specialist can do without knowledge of physics, whose experience in cargo transportation allows you to intuitively determine the maximum volume allowed for transportation.

The scientific method involves knowledge of such a parameter as the load.

The formula V=m/ρ is used, where m is the mass of the load, ρ is the density of the material. Before calculating the volume, it is worth knowing the density of the load, which is also not at all difficult (tables, laboratory definition).

This technique also works remarkably well in determining volumes of liquid cargoes. The liter is used as the unit of measure.

Determining the volume of building forms

The issue of determining volumes plays an important role in construction. The construction of houses and other structures is a costly business, building materials require careful attention and extremely accurate calculation.

The basis of the building - the foundation - is usually a cast structure filled with concrete. Before that, you need to determine the type of foundation.

The slab foundation is a slab in the form of a rectangular parallelepiped. Columnar base - rectangular or cylindrical pillars of a certain section. By determining the volume of one column and multiplying it by the quantity, it is possible to calculate the cubic capacity of concrete for the entire foundation.

When calculating the volume of concrete for walls or ceilings, they do it quite simply: determine the volume of the entire wall, multiplying the length by the width and height, then separately determine the volumes of window and door openings. The difference between the volume of the wall and the total volume of openings is the volume of concrete.

How to determine the volume of a building?

Some applied tasks require knowledge about the volume of buildings and structures. These include problems of repair, reconstruction, determination of air humidity, issues related to heat supply and ventilation.

Before answering the question of how to calculate the volume of a building, measurements are taken on its outer side: the cross-sectional area (length multiplied by the width), the height of the building from the bottom of the first floor to the attic.

The determination of the internal volumes of heated premises is carried out by internal strokes.

The device of heating systems

Modern apartments and offices cannot be imagined without a heating system. The main part of the systems are batteries and connecting pipes. How to calculate the volume of the heating system? The total volume of all heating sections, which is indicated on the radiator itself, must be added to the volume of pipes.

And at this stage the problem arises: how to calculate the volume of the pipe. Imagine that the pipe is a cylinder, the solution comes by itself: we use the cylinder formula. In heating systems, pipes are filled with water, so it is necessary to know the area of ​​\u200b\u200bthe internal section of the pipe. To do this, we determine its inner radius (R). The formula for determining the area of ​​a circle: S=πR 2 . The total length of the pipes is determined by their length in the room.

Sewerage in the house - pipe system

When laying pipes for drainage, it is also worth knowing the volume of the pipe. At this stage, an outer diameter is needed, the steps are similar to the previous ones.

Determining the volume of metal that goes into the manufacture of the pipe is also an interesting task. Geometrically, a pipe is a cylinder with voids. Determining the area of ​​a ring lying in its cross section is a rather complicated task, but it can be solved. A simpler way out is to determine the external and internal volumes of the pipe, the difference between these values ​​\u200b\u200band will be the volume of the metal.

Determination of volumes in problems of physics

The famous legend about the crown of King Heron became famous not only as a result of solving the problem of bringing thieving jewelers “to clean water”. The result of the complex mental activity of Archimedes is the determination of the volumes of bodies of irregular geometric shape. The main idea extracted by the philosopher is that the volume of liquid displaced by the body is equal to the volume of the body.

In laboratory studies, a measuring cylinder (beaker) is used. The volume of liquid is determined (V 1), the body is immersed in it, secondary measurements are performed (V 2). The volume is equal to the difference between the secondary and primary measurements: V t \u003d V 2 - V 1.

This method of determining the volumes of bodies is used in calculating the bulk density of bulk insoluble materials. It is extremely convenient in determining the density of alloys.

You can calculate the volume of a pin using this method. It seems difficult enough to determine the volume of such a small body as a pin or a pellet. It cannot be measured with a ruler, the measuring cylinder is also large enough.

But if you use several completely identical pins (n), then you can use a graduated cylinder to determine their total volume (V t \u003d V 2 - V 1). Then divide the resulting value by the number of pins. V= V t \n.

This task becomes clear if it is necessary to cast many pellets from one large piece of lead.

Liquid volume units

The international system of units assumes the measurement of volumes in m 3. In everyday life, off-system units are more often used: liter, milliliter. When it is determined how to calculate the volume in liters, the conversion system is used: 1 m 3 \u003d 1000 liters.

The use of other non-systemic measures in everyday life can cause difficulties. The British use barrels, gallons, bushels, which are more familiar to them.

Translation system:

Tasks with non-standard data

Task 1. How to calculate the volume, knowing the height and area? Typically, this problem is solved by determining the amount of coating of various parts by galvanization. The surface area of ​​the part (S) is known. Layer thickness (h) - height. Volume is determined by the product of area and height: V=Sh.

Problem 2. For cubes, the problem of determining the volume may look interesting, from a mathematical point of view, if the area of ​​\u200b\u200bone face is known. It is known that the volume of a cube is: V=a 3 , where a is the length of its face. The area of ​​the side surface of the cube S=a 2 . Extracting from the area, we get the length of the face of the cube. We use the volume formula, calculate its value.

Task 3. Calculate the volume of a figure if the area is known and some parameters are given. Additional parameters include conditions for the ratio of sides, heights, base diameters, and much more.

To solve specific problems, you will need not only knowledge of the formulas for calculating volumes, but also other geometry formulas.

Determining the amount of memory

A task completely unrelated to geometry: to determine the amount of memory of electronic devices. In the modern, fairly computerized world, this problem is not superfluous. Precise devices, such as personal computers, do not tolerate approximation.

Knowing the amount of memory on a flash drive or other storage device is useful when copying or moving information.

It is important to know the amount of RAM and permanent memory of the computer. Often the user is faced with a situation where “the game is not running”, “the program hangs”. The problem is quite possible with a low amount of memory.

A byte and its derivatives (kilobyte, megabyte, terabyte) are considered.

1 kB = 1024 B

1 MB = 1024 kB

1 GB = 1024 MB

The strangeness in this recalculation system follows from the binary information encoding system.

The memory size of a storage device is its main characteristic. Comparing the amount of information transferred and the amount of memory of the drive, you can determine the possibility of its further operation.

The concept of "volume" is so broad that it is possible to fully understand its versatility only by solving applied problems, interesting and exciting.

They are the most common type of cardboard boxes in Ukraine. Such boxes are used for a variety of purposes - they have proven themselves equally well for packaging finished products, and for transport operations, and as a "container for everything in the world." At the same time, the range of goods and types of products that are packed in cardboard boxes is very extensive and varied. Thus, corrugated cardboard boxes are used for packaging of oversized and oversized cargo, as well as cargo of various weights. This point is very important to understand before calculating the volume of the box you need.

Why is it important to know the exact volume of a rectangular box?

As we noted earlier, cardboard boxes are mainly used for the storage and transportation of goods and cargo. Imagine that you are engaged in the production of any product, while you can use just the same huge warehouse to store finished products, but we guarantee you that sooner or later you will not have enough space for the entire range of products. Or you are the owner of a store, for example, household goods. In any case, you will try to expand the range to increase sales and, as a result, profit - which means you just need to have at least a few copies of each item on hand, in the back room of the store. Both of these examples (large and medium-sized businesses) clearly show that without taking into account the total volume of packaged finished products, it is almost impossible to establish an uninterrupted operation of the enterprise - everything must fit and everything must be sold.

In addition to storage, knowing the volume of your packaged products will come in handy in the shipping process. It should be noted right away that the type of transport here should mean literally everyone - the transportation of packaged goods by road, by plane, by ship, and by rail is carried out based on two main parameters - the volume of cargo and its weight. At the same time, it does not matter which shipping company you choose to deliver your products - volume, as the main value for assessing the cargo and, as a result, the cost of its transportation, is used by both private and state transport and postal companies.

Calculation of the volume of standard boxes of rectangular and square shape

This type of volume calculation is perhaps the simplest, since we are all familiar with it from school. The volume in this case reflects the dimensions of the object in a three-dimensional plane and for any rectangular or square cardboard box will determine its capacity. To determine the volume, you need to perform a few simple calculations: measure the length, width and height of the box, and then multiply the resulting values. If you are going, knowing only the dimensions of the product or cargo that will be packed in it, then you should measure the dimensions of the cargo and add 5-10 millimeters to each of the values ​​\u200b\u200b(length, width, height), and then multiply the resulting values.

Now let's more clearly and step by step analyze these mathematical operations:

In the international measurement system, to calculate the volume of a rectangular or square object (in our case, a cardboard box), the formula is used: Vm3 = L x W x H

• V is, in fact, the volume that we need to calculate
• L - box length
• W - box width
• H - the height of the box (the term "depth" can also be used, which, in general, is the same thing)

Let's analyze this formula for calculating the volume of cardboard boxes using a specific example with explanations. Suppose you want to calculate the volume of a four-valve carton box for packaging, say, electronics and home appliances. How to do it? We answer.

To begin with, you should immediately decide which units of measure you will use in your measurements - meters, centimeters or millimeters. It is important that all measurements of the parameters of your box are in the same value - in order to avoid inaccuracies and confusion. And the second important point is the internal and external dimensions of the box. To accurately measure the volume of a cardboard box, you need to figure out why you need the exact volume of this box. If you want to know the volume in order to accurately calculate the size of the cargo that will be packed in it, then use the internal dimensions. And if you need, in order to fill the vehicle body with products packed in such boxes as much as possible, then use the external dimensions.

This point is very important if you want to get accurate data without any margin of error.

We figured out the theory, now we turn to practical actions - we measure our box and calculate its volume.

Step #1

First you need to measure the length of the box. Look at the box from top to bottom and you will see that it has the shape of an equilateral rectangle. The longest side of the box is the length, denoted by the letter "L" (from the English "length" - length). Measure and record the result of the measurement somewhere - so as not to forget.

Step #2

Next, measure the width of our box. In any rectangular cardboard box, the shorter side is the width. According to the international measurement system, the width of a cardboard box is indicated by the letter "W" (from the English "width" - width). Measure and record the measurement result somewhere - so as not to forget. And remember about the same units of measurement for all measurements. For a square-shaped cardboard box, the “length” and “width” values ​​are the same, so you just need to measure one side of the corrugated cardboard box once and substitute the resulting size as both the length and the width of the box.

Step #3

We measure the height of our cardboard box. The height of a rectangular or square carton is usually the size of the side perpendicular to the flaps of the box. According to the international measurement system, the width of a cardboard box is indicated by the letter "H" (from the English "height" - height). The height of the cardboard box is taken as the distance from the top flap of the box to the bottom flap. Measure and record the measurement result somewhere - so as not to forget.

Step #4

Since all the quantities of interest to us have been determined and measured, we proceed directly to calculating the volume of interest to us for the packaging of electronics and electrical appliances.

According to the international measurement system, the volume of a cardboard box is indicated by the letter "V" (from the English "volume" - volume) and is calculated by multiplying the length, width and height of the box.

In the process of measurements, we found out that the size of the box, let's say, is 600 x 400 x 400 millimeters. Next, we substitute these values ​​into the formula: Vm3 = L x W x H.

We get:

600 x 400 x 400 \u003d 96000000 mm3, which in terms of cubic meters is - 0.096 m3.

Step #5

Now it remains only to convert the volume of the cardboard box from cubic meters to liters. If the indication of cubic units of volume allows you to understand how many such cubes can be placed inside the box, then the value in liters makes it possible to calculate the volume of the box for packing small and bulk goods and cargo, for example, groceries and various cereals.

1 m3 = 1000 liters

Substitute our values ​​into this formula and get:

0.096 m3 cardboard box = 96 liter corrugated cardboard box.

That, in fact, is all! Now you know how to calculate the volume of a rectangular or square cardboard box. In the final part of the article, the editors of the Express Packing online store will tell you how to calculate any volume. For example, the volume of a cardboard box with a complex die-cut shape, or self-assembly.

The most common question from customers is how to calculate the volume of cargo. The question is legitimate, since the choice of transport depends on the result of the calculation, and there is always the opportunity to choose a car from a cheaper range of models.

Each vehicle can carry a certain weight and cubic capacity, the parameters are usually indicated on the car body, but if you have any questions, you can always ask them to the managers of KVAD Logistics.

How to calculate the volume of cargo yourself?

If it is not difficult to weigh items for transportation, then certain problems arise with the calculation of volume.

Any object, if it occupies a separate space, has its maximum length, width and height in certain places. For example, if you are going to transport a statue, then it cannot be folded with some other object, thereby saving space. Therefore, its volume is considered separately. The width of the widest place is taken as the width, the height is considered from the floor to the highest point, the length is measured in a position perpendicular to the width vector parallel to the floor according to the same principle: the widest place is searched.

Items that can be nested in each other, for example, frames and corners, building blocks, can be considered as a single value, adding 20-30% to the volume for packaging and placement in the truck.

The calculation of the cargo volume is very simple: the length is multiplied by the width and by the height. The resulting figure is converted into square meters.

If the load is not heavy, then voluminous and fairly light structures, for example, furniture, can be taken away in a small truck with a low carrying capacity. If, in addition to volume, objects will have a lot of weight, more powerful transport will be needed.

After calculating the volume of all types of cargo, the volumes are summarized. The resulting value is multiplied by 1.3. Tolerance is required because the load cannot be placed side by side, unless they are boxes of the same size. The allowed space is allocated to the voids that are formed during loading of uneven cargo.

Of course, this is a very rough estimate. The packaged cargo will have different volumes, and the packaging itself, perhaps, will somehow make it possible to create more capacious dimensions.

How to calculate the volume of cargo correctly?

If you need to transport cargo over a long distance, entrust the calculations to determine the volume of cargo to the professionals of KVAD Logistics.

Since the cargoes are sent simultaneously by many clients of the company, it is possible to place compact cargoes in one transport, and overall and heavy ones in another. As a result, you will have to pay less, since the transportation costs will be distributed more evenly and among all participants in proportion to the weight and volume of the shipped products. You do not need to think about how to calculate the volume of cargo. We will carry out this procedure for you and select the most profitable transportation options for you.

The cost of delivery of goods is an important issue that interests many of our customers. Most transport companies price their services based on the volume of cargo in cubic meters - in other words, the volume of the space that the packaged cargo will occupy in the transport compartment of an aircraft, a sea container, a freight truck or a railway wagon.

Which delivery to choose - air, railway or car?

In order to navigate the prices for delivery and choose the most optimal mode of transport when ordering goods from China, you need to know the total volume of cargo in m 3 that you want to receive. A calculator on our website will help you calculate the volume, but in order to quickly get the desired result, you must use the following data:

• type of packaging (box or cylinder);
• basic packaging parameters - length, width and height (for boxes) or height and diameter (for cylinders);
• number of packages in pieces.

By measuring the main packaging parameters with a ruler, you can calculate the volume of a box or cylinder, and then calculate the volume of the entire consignment in cubic meters. The figures obtained will help you compare the prices for delivery by one or another transport and choose the appropriate option.

Why do you need a volume calculator?

One of the main qualities of a modern businessman is the ability to quickly make important decisions and respond in a timely manner to changes in market trends. Our volume calculator helps you save time on calculations and get the numbers you need in just a few minutes.

Using the volume calculator is convenient and very simple: for calculations, enter the necessary numbers in the appropriate fields, and then feel free to click on the "Calculate" button. The volume calculator in m 3 gives the finished result, regardless of the units of measurement in which you entered the tare parameters - in centimeters or meters. The system automatically converts the data into the required format and displays the final result in cubic meters.

Knowing the volume of containers and the total volume of cargo, you can correctly choose the appropriate type of transport and place the goods in it as compactly as possible without overpaying for empty space. Use the online packaging volume calculator to quickly calculate the volume of a box or tubes, as well as the entire batch of goods. The second calculator will help you find out the estimated cost of shipping cargo from China by various modes of transport, taking into account its volume in m 3.

How to calculate the volume of a box?

In order to calculate the volume of a box, it is necessary to measure its length, height and width. If you have a sample of packaging for your products, use a ruler to measure. Information about the parameters of the box can also be obtained from the supplier. There are two ways to calculate the volume of a box in cubic meters: using our online volume calculator in m 3 or using the formula yourself. Let's consider both options.

• In order for the volume calculator to correctly calculate the volume of the box, select the option "Box volume". Measure the box, focusing on the image next to the calculator (or copy the information about its parameters from the seller’s website), and enter the numbers into the volume calculation calculator. You can also specify the number of boxes and shipping costs per cubic meter. Click on the "Calculate" button - in the table below you will see the final result: the volume of the box in m 3. If you provided data on the number of boxes and the cost of delivery for calculations, then the plate will also show the total volume of cargo and the estimated amount of delivery.
• You can independently calculate the volume of packaging using the formula that is studied in mathematics lessons at school: V = a * b * h. Here V is the volume, a is the length, b is the width and h is the height (note: all data obtained during measurements must be converted from centimeters to meters). Just multiply these numbers and you will get the required volume of the box in cubic meters.

How to calculate the volume of a cylinder (pipe)?

Your goods will be packed in a cylindrical container, and you want to know the volume of cargo? The calculator will easily cope with this task. For calculations, you will need parameters such as the height of the container and its diameter. Use a ruler to measure, as in the case of a box, or ask the supplier for packaging parameters. Next, our calculator for calculating the volume will be used:

• mark the type of container (cylinder/pipe);
• enter the packaging parameters in the appropriate lines;
• indicate the number of pipes (if you know it);
• click the "Calculate" button.

Done: the calculator calculated the volume of cargo in a second! The table with the results shows the volume in cubic meters of both one pipe and the total volume of your cargo (if the number of packages was indicated).

For independent calculations and consolidation of knowledge gained at school, use the formula V=π*r 2 *h. As we remember, V denotes volume, π is the number "pi" equal to 3.14, r 2 is the radius of the pipe squared, and h is its height. Multiplying all the numbers, you get the volume of the container of a cylindrical shape. Do not forget: after measuring the radius of the pipe and its height, convert centimeters to meters - and then you will get the correct result in m 3.

How to calculate the volume of cargo in different containers?

It's good when the entire load has the same dimensions - the online volume calculator solves such problems in a matter of seconds. And how to calculate the volume of cargo if it is packed in containers of various shapes - large and small boxes and cylinders?

There is nothing complicated here, the main thing is to know the exact parameters of each type of container and its quantity. Our volume calculator in m 3 will help you quickly calculate the volume of cargo packed in containers of the same shape and size, after which all you have to do is add up all the numbers and get the total volume of your cargo.

How to calculate shipping cost?

Knowing the total volume of cargo in cubic meters, you can easily navigate the cost of delivery from China by various means of transport. To do this, use the calculation results provided by our volume calculator. In a special form located under the calculator, enter the received numbers in the "Volume" field. Select the delivery option (by sea, by air, by road, etc.), enter the points of departure and destination, and fill in other fields, then click the "Calculate" button. The system will automatically calculate the cost of shipping your cargo for the selected shipping option.

We will help you figure out how to correctly calculate the volume of transported cargo. This procedure is very important in order to avoid misunderstandings when loading containers or boxes of products into a vehicle. Thanks to modern technologies, it will not be difficult to calculate the volume, the main thing is your presence on our page.

The essence of the calculation of volumes and their role in the delivery process

Volume calculation is an important part of the delivery process, so the calculations must be carried out professionally and without errors. When calculating, it is necessary to indicate all dimensions that must be converted in advance to cubic meters. As practice has shown, this task is not feasible for everyone. At school, we were taught how to translate indicators into m3, but not everyone understands this. The volume of the cargo must be converted to m3 in order to know what area the box will occupy upon delivery.

What is the purpose of calculating cubic capacity?

The cubic capacity must be calculated in order to make a correct and competent application for the transportation. Also, knowing the volume of cargo in cubic meters, you can decide which type of transportation to choose.

How to make calculations and what is their importance?

First of all, let's recall the definition of volume, what it is and what formula it is calculated by. However, there are times when certain difficulties arise when calculating the volume. This is due to the boxes of non-standard shape. Calculating the volume of an ordinary rectangular box will not be difficult, but the volume of boxes with non-standard shapes requires more care, there are special formulas for this. First you need to know the shape of the box. Consider what forms the boxes are:

• cube shaped box
• cylindrical box
• rectangular box
• box with the shape of a truncated pyramid (very rare)

After determining the shape, measurements of the box are taken. It is important to make accurate measurements to avoid error.

Why do you need to know the volume?

Knowing the exact volume of the box, you can avoid problems during the loading of products into the vehicle. Little depends on the volume of the box itself, the main component is the size of the goods itself. If you ask why? We will answer, because initially it is necessary to focus on the dimensions of the cargo, for which the appropriate box will be selected. Knowing the dimensions of the cargo, you can calculate its volume in order to select the required box. Thus, we translate the volume of cargo into cubic meters, the special formula V = a * b * h will help us with this. As you can see, everything is easy.

It is also important to remember that in order to correctly determine the choice of transport, it is necessary to convert the volume of cargo into cubic meters. It is not difficult to carry out this calculation, for this you just need to first measure the dimensions of the cargo and multiply these indicators. To correctly calculate the delivery, it is imperative to convert units to m3.

What to do if the box is round instead of rectangular? This situation is rare, but still it cannot be ruled out. In this case, it is necessary to calculate the volume of the container or box with a circle at the base. The following formula will help with this: V *r2*h. Do not forget, you must first correctly measure the parameters of the load.

And now we remember the lessons of mathematics!

The most frequently asked question is: “how to calculate the volume correctly?”. First of all, it is necessary to determine the volume of what needs to be calculated, namely, the shapes of what shape. Our site will also help you learn how to calculate the total volume of the cargo and the box itself.

What are the most common problems you encounter?

The confusion may lie in determining whether this figure is voluminous or flat. Calculating the volume itself is already the second question, initially you need to know the exact dimensions, remember that there are always three of them.

Now the question of delivery. Having made the necessary calculations of the volume of cargo, it is important to determine the type of delivery. This is a very important question in which no mistakes can be made. Therefore, in order to avoid shortcomings, it is necessary to accurately calculate the volume of cargo, after which, focusing on specific numbers, you can safely choose the type of transport.

Which mode of transport is right for you?

It is important to remember that the delivery process includes not only the correct calculation of cubic capacity, but also focuses on the specific placement of products. You have already familiarized yourself with the process of calculations and determination of cubic capacity, now the choice of a vehicle depends only on you.

In the world, quite a lot of objects have a cylindrical shape, the volume of which has to be calculated periodically. It can be a culinary task, or it can be useful in construction. In this case, the scope of use is not so important, but the calculation method is important. In mathematics, which describes various objects and phenomena of our life, theorems and formulas act as such means.

Algorithm for determining the volume of a cylinder

Let us return to the procedure for calculating the volume of a cylinder if its height and radius are known. To begin with, you need to answer a number of easy questions. First you need to determine which cylinder is in front of you.

The classic ideal variant is often considered, when a cylinder is obtained by rotating a rectangle around one of its sides, and then the bases are circles whose radii are equal to each other, and the generatrix will be the height. Such a cylinder is called a round straight.

The second task in determining the volume of a cylinder is finding the height. Using the rule will be easier than ever. It is enough just to connect the centers of the circles to each other.

How to calculate the volume of a round straight cylinder

The volume of a round straight cylinder is the product of the area of ​​the circle at the base of the cylinder times the height and is expressed by the following formula:

V \u003d P * R 2 * Η, where:

• V is the volume of the cylinder;
• Π = 3, 14 and is a constant value;
• R - radius;
• H - height.

Solution: V \u003d 3.14 * 6 * 2 * 2 \u003d 75.36 cm 3.

How to calculate the volume of a truncated circular cylinder

The situation changes if we are dealing with a truncated round cylinder. A distinctive feature of this type of cylinder from the classical one may be that its bases do not lie on parallel planes, and therefore the formula for calculating the volume of a cylinder takes on a slightly different form:

V \u003d P * R 2 * (H 1 + H 2) / 2, where:

• V is the volume of the cylinder;
• R - radius;
• H1 - high altitude;
• H2 - lower height.

Solution: V \u003d 3.14 * 3 * 3 * (5 + 3) / 2 \u003d 113.04 cm 3.

The heights are numbered arbitrarily, so that the order can be chosen by the participant to solve a specific problem. As you know, the amount does not change from the rearrangement of places.

There are other types of cylinders, for example: elliptical, parabolic and hyperbolic. They are described by second-order equations, and completely different parameters are needed to calculate their volume.

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How to distinguish a person with a technical specialty from a person with a humanitarian mindset? Ask everyone what a cylinder is. The first will say that this is a geometric body, the second will remember the men's headdress of the 19th century. Both will be right, and the hat got its name due to its special shape, the basis of which was the same figure from geometry. So, what are the features of a cylinder and how to calculate its volume.

Cylinder Volume Calculation

The word "cylinder" comes from the ancient Greek kylindros, meaning "roller". Mathematicians give several definitions for a cylinder:

1. A cylinder is a geometric body bounded by a cylindrical surface and two parallel planes intersecting it at right angles.
2. A cylinder is a body of revolution, which is obtained by rotating a rectangle around its side.
3. A cylinder is a geometric body that is formed by rotating a rectangle on an axis coinciding with one of its sides.

All of these definitions are correct. It is also worth noting the main parts of the cylinder:

1. Bases are flat figures formed by the intersection of a cylindrical surface with two parallel planes.
2. The lateral surface of the cylinder is the surface between the planes of the bases.

If the base of the cylinder is a circle, then it is called circular. There are other types of cylinders, depending on the shape of the base - elliptical, hyperbolic, parabolic, etc.

Also, all cylinders are divided into straight and inclined. Each cylinder has generators - these are segments connecting the corresponding points of the bases. If the generators are perpendicular to the bases, then the cylinder is called straight, and if the generators are located at an angle, the cylinder is inclined or oblique.

There are other general concepts for cylinders:

1. The bases of the cylinder are equal and lie in parallel planes. In a cylinder, the generators are parallel and equal.
2. The surface of a cylinder consists of bases and a side surface. The lateral surface is composed of generators.
3. The radius of a cylinder is the radius of its base.
4. The height of the cylinder is the distance between the planes of the bases.
5. The axis of a cylinder is a straight line passing through the centers of the bases.
6. The section of a cylinder by a plane passing through the axis of the cylinder is called an axial section.
7. The plane passing through the generatrix of a straight cylinder and perpendicular to the axial section drawn through this generatrix is ​​called the tangent plane of the cylinder.

So how do you calculate the volume of a cylinder? You can calculate the volume of a right circular cylinder using a calculator. It is equal to the product of the area of ​​the base and the height.

where V is the volume of the cylinder, R is the radius of the base, h is the height of the cylinder, and "pi" is a constant equal to 3.14.

In the same way, the volume of a right circular cylinder is calculated through the diameter of the base circle - d.

If the cylinder is straight, but not circular, then the formula for calculating the volume is the product of the length of the generatrix - n and the cross-sectional area of ​​\u200b\u200bthe cylinder with a plane perpendicular to the generatrix - S.

If the cylinder is inclined, then the sine of the angle of inclination (alpha) of the generatrix to the base also participates in the formula. In this case, the volume is calculated by the formula:

V = S*n*sinα

The volume of a cylinder is calculated in cubic units.

If the task is to find the volume of a cylinder circumscribed around the sphere, then the calculations will be as follows:

The radius of the cylinder is equal to the radius of the sphere - R. The height of the cylinder is equal to the diameter of the sphere. The diameter is twice the radius - 2R. Thus, the volume of a straight circumscribed cylinder is equal to the product of the base area πR2 (“pi” times the radius squared) times the height, i.e. 2R.

Bringing the formula to the proper form, we get:

If the cylinder is inscribed in a rectangular parallelepiped, then, knowing the length of the side of its base and the height, you can find the volume.

In this case, the radius of the base of the cylinder is equal to half the length of the side of the base of the parallelepiped - a. The height of the cylinder and the parallelepiped are the same, denoted by h. Then the volume is calculated by the formula:

Where is the calculation of the volume of a cylinder used?

Calculation of the volume of the cylinder students are in high school. In adulthood, this knowledge is used in their work by engineers and designers of various machines and mechanisms, consumer goods, as well as architects.

From consumer goods, glasses, mugs, glasses, pots, thermoses and other utensils, as well as some vases, cans and packaging of drinks or household chemicals have a cylindrical shape. The volume of such cylindrical objects is calculated in liters.

The volume of the cylinder is calculated in the production of medical syringes. The exact amount of medication administered to the patient during injection depends on the volume received. Medicines in liquid form, suspensions, solutions are placed in cylindrical glass or plastic bottles, and the volume of the product is indicated on the tag.

Cylinders are also common in technology: shafts and their individual components used in internal combustion engines have this type. In addition, the calculation of the cylinder volume is a task that designers have to solve when designing modern gasoline and diesel power units, because the characteristics, first of all, power depend on this parameter. Internal combustion engines are equipped with pistons, which also have a cylindrical shape.

Architects have to calculate the volume of a cylinder when designing buildings with columns. True, these architectural elements in the classical version (together with the base and the capital) are rare, but simplified varieties consisting of a single trunk (which is a cylinder) are often used.

Extremely common parts that are present in the designs of technical devices are roller bearings. As you might guess from the name, the main component is strong and wear-resistant metal cylindrical rollers. Thanks to this geometry, these parts have a high load-bearing capacity and are able to withstand loads. Roller bearings are high-precision parts, and therefore, when creating them, the correct calculation of the volume of the cylinder (roller) plays an important role.

Reservoirs and tanks are used to transport and store various types of fuels, oil, water and gas, some building materials, chemicals, and foodstuffs. Many do not know how to calculate the volume of a container, because they can have a different geometric shape:

• Cone;
• cylinder;
• Spheres;
• Rectangular parallelepiped.

In our article, we will get acquainted with the nuances of the calculation for specific geometric bodies.

How to find out the volume of a rectangular container

In the field of construction, all volume indicators are reduced to specific values. Calculations can be made in liters or dm 3 , but most often cubic meters are used to determine the amount of a material. How to calculate the cubature of the simplest rectangular containers will be described further with a specific example.

For work, we need a container, a construction tape measure and a notebook with a pen or pencil for calculations. From the course of geometry it is known that the volume of such bodies is calculated by multiplying the length, width and height of the product. The calculation formula is as follows

V=a*b*c, where a, b and c are the sides of the container.

For example, the length of our product is 150 centimeters, the width is 80 centimeters, the height is 50 centimeters. For the correct calculation of the cubature, we translate the indicated values ​​into meters and carry out the necessary calculations V = 1.5 * 0.8 * 0.5 = 0.6 m3.

How to determine the volume of a spherical product

Spherical products are found in our lives almost every day. It can be a bearing element, a soccer ball or the writing part of a ballpoint pen. In some cases, we need to know how to calculate the cubature of a sphere to determine the amount of liquid in it.

According to experts, to calculate the volume of this figure, the formula is used V=4/3ԉr3, where:

• V is the calculated volume of the part;
• R is the radius of the sphere;
• ԉ is a constant value equal to 3.14.

To carry out the necessary calculations, we need to take a tape measure, fix the beginning of the measuring scale and measure it, and the tape tape must pass along the equator of the ball. After that, the diameter of the part is found out by dividing the size by the number ԉ.

And now let's get acquainted with a specific example of calculating for a sphere if its circumference is 2.5 meters. First, we determine the diameter of 2.5 / 3.14 \u003d 0.8 meters. Now we substitute this value into the formula:

V= (4*3.14*0.8³)/3=2.14m³

How to calculate the volume of a tank made in the form of a cylinder

Similar geometric shapes are used for food storage, fuel transportation and other purposes. Many do not know how to calculate the volume of water, but we will describe the main nuances of such a process later in our article.

The height of the liquid in a cylindrical container is determined by a special device called a measuring rod. In this case, the capacity of the tank is calculated according to special tables. Products with special tables for measuring volume are rare in life, so let's approach the solution of the problem in a different way and describe how to calculate the volume of a cylinder using a special formula - V \u003d S * L, where

• V is the volume of the geometric body;
• S is the cross-sectional area of ​​the product in specific units of measurement (m³);
• L is the length of the tank.

The L indicator can be measured using the same tape measure, but the cross-sectional area of ​​\u200b\u200bthe cylinder will have to be calculated. The S index is calculated by the formula S=3.14*d*d/4, where d is the diameter of the cylinder circumference.

Now let's take a look at a specific example. Let's say the length of our tank is 5 meters, its diameter is 2.8 meters. First, we calculate the cross-sectional area of ​​\u200b\u200bthe geometric figure S = 3.14 * 2.8 * 2.8 / 4 = 6.15 m. And now you can start calculating the volume of the tank 6.15 * 5 = 30.75 m³.