Cylinder lateral surface area calculator. Cylinder radius, online calculation

It is a geometric body bounded by two parallel planes and a cylindrical surface.

The cylinder consists of a side surface and two bases. The formula for the surface area of ​​a cylinder includes a separate calculation of the area of ​​the bases and the lateral surface. Since the bases in the cylinder are equal, then its total area will be calculated by the formula:

We will consider an example of calculating the area of ​​\u200b\u200ba cylinder after we know all the necessary formulas. First we need the formula for the area of ​​the base of a cylinder. Since the base of the cylinder is a circle, we need to apply:
We remember that these calculations use a constant number Π = 3.1415926, which is calculated as the ratio of the circumference of a circle to its diameter. This number is a mathematical constant. We will also consider an example of calculating the area of ​​​​the base of a cylinder a little later.

Cylinder side surface area

The formula for the area of ​​the lateral surface of a cylinder is the product of the length of the base and its height:

Now consider a problem in which we need to calculate the total area of ​​a cylinder. In a given figure, the height is h = 4 cm, r = 2 cm. Let's find the total area of ​​the cylinder.
First, let's calculate the area of ​​the bases:
Now consider an example of calculating the lateral surface area of ​​a cylinder. When expanded, it is a rectangle. Its area is calculated using the above formula. Substitute all the data into it:
The total area of ​​a circle is the sum of twice the area of ​​the base and the side:

Thus, using the formulas for the area of ​​the bases and the lateral surface of the figure, we were able to find the total surface area of ​​the cylinder.
The axial section of the cylinder is a rectangle in which the sides are equal to the height and diameter of the cylinder.

The formula for the area of ​​the axial section of a cylinder is derived from the calculation formula:

How to calculate the surface area of ​​a cylinder is the topic of this article. In any mathematical problem, you need to start with data entry, determine what is known and what to operate on in the future, and only then proceed directly to the calculation.

This three-dimensional body is a geometric figure of a cylindrical shape, bounded above and below by two parallel planes. If you apply a little imagination, you will notice that a geometric body is formed by rotating a rectangle around an axis, with the axis being one of its sides.

It follows from this that the described curve above and below the cylinder will be a circle, the main indicator of which is the radius or diameter.

Cylinder Surface Area - Online Calculator

This function finally facilitates the calculation process, and everything comes down to automatic substitution of the given values ​​of the height and radius (diameter) of the base of the figure. The only thing that is required is to accurately determine the data and not make mistakes when entering numbers.

Cylinder side surface area

First you need to imagine how the sweep looks in two-dimensional space.

This is nothing more than a rectangle, one side of which is equal to the circumference. Its formula has been known since time immemorial - 2π *r, where r is the radius of the circle. The other side of the rectangle is equal to the height h. It won't be hard to find what you're looking for.

Sside= 2π *r*h,

where number π = 3.14.

Full surface area of ​​a cylinder

To find the total area of ​​the cylinder, you need to get S side add the areas of two circles, the top and bottom of the cylinder, which are calculated by the formula S o =2π*r2.

The final formula looks like this:

Sfloor\u003d 2π * r 2+ 2π*r*h.

Cylinder area - formula in terms of diameter

To facilitate calculations, it is sometimes necessary to make calculations through the diameter. For example, there is a piece of a hollow pipe of known diameter.

Without bothering with unnecessary calculations, we have a ready-made formula. Algebra for 5th grade comes to the rescue.

Sgender = 2π*r 2 + 2 π*r*h= 2 π*d 2 /4 + 2 π*h*d/2 = π*d 2 /2 + π *d*h,

Instead of r in the full formula you need to insert the value r=d/2.

Examples of calculating the area of ​​a cylinder

Armed with knowledge, let's get down to practice.

Example 1 It is necessary to calculate the area of ​​a truncated piece of pipe, that is, a cylinder.

We have r = 24 mm, h = 100 mm. You need to use the formula in terms of the radius:

S floor \u003d 2 * 3.14 * 24 2 + 2 * 3.14 * 24 * 100 \u003d 3617.28 + 15072 \u003d 18689.28 (mm 2).

We translate into the usual m 2 and get 0.01868928, approximately 0.02 m 2.

Example 2 It is required to find out the area of ​​​​the inner surface of the asbestos stove pipe, the walls of which are lined with refractory bricks.

The data are as follows: diameter 0.2 m; height 2 m. We use the formula through the diameter:

S floor \u003d 3.14 * 0.2 2 / 2 + 3.14 * 0.2 * 2 \u003d 0.0628 + 1.256 \u003d 1.3188 m 2.

Example 3 How to find out how much material is needed to sew a bag, r \u003d 1 m and a height of 1 m.

One moment, there is a formula:

S side \u003d 2 * 3.14 * 1 * 1 \u003d 6.28 m 2.

Conclusion

At the end of the article, the question arose: are all these calculations and translations of one value into another really necessary? Why is all this necessary and most importantly, for whom? But do not neglect and forget simple formulas from high school.

The world has stood and will stand on elementary knowledge, including mathematics. And, when embarking on some important work, it is never superfluous to refresh the data of calculations in memory, applying them in practice with great effect. Accuracy - the politeness of kings.

A cylinder is a geometric body bounded by two parallel planes and a cylindrical surface. In the article, we will talk about how to find the area of ​​a cylinder and, using the formula, we will solve several problems for example.

A cylinder has three surfaces: a top, a bottom, and a side surface.

The top and bottom of the cylinder are circles and are easy to define.

It is known that the area of ​​a circle is equal to πr 2 . Therefore, the formula for the area of ​​two circles (top and bottom of the cylinder) will look like πr 2 + πr 2 = 2πr 2 .

The third, side surface of the cylinder, is the curved wall of the cylinder. In order to better represent this surface, let's try to transform it to get a recognizable shape. Imagine that a cylinder is an ordinary tin can that does not have a top lid and bottom. Let's make a vertical incision on the side wall from the top to the bottom of the jar (Step 1 in the figure) and try to open (straighten) the resulting figure as much as possible (Step 2).

After the full disclosure of the resulting jar, we will see a familiar figure (Step 3), this is a rectangle. The area of ​​a rectangle is easy to calculate. But before that, let us return for a moment to the original cylinder. The vertex of the original cylinder is a circle, and we know that the circumference of a circle is calculated by the formula: L = 2πr. It is marked in red in the figure.

When the side wall of the cylinder is fully expanded, we see that the circumference becomes the length of the resulting rectangle. The sides of this rectangle will be the circumference (L = 2πr) and the height of the cylinder (h). The area of ​​a rectangle is equal to the product of its sides - S = length x width = L x h = 2πr x h = 2πrh. As a result, we have obtained a formula for calculating the lateral surface area of ​​a cylinder.

The formula for the area of ​​the lateral surface of a cylinder
S side = 2prh

Full surface area of ​​a cylinder

Finally, if we add up the area of ​​all three surfaces, we get the formula for the total surface area of ​​a cylinder. The surface area of ​​the cylinder is equal to the area of ​​the top of the cylinder + the area of ​​the base of the cylinder + the area of ​​the side surface of the cylinder or S = πr 2 + πr 2 + 2πrh = 2πr 2 + 2πrh. Sometimes this expression is written by the identical formula 2πr (r + h).

The formula for the total surface area of ​​a cylinder
S = 2πr 2 + 2πrh = 2πr(r + h)
r is the radius of the cylinder, h is the height of the cylinder

Examples of calculating the surface area of ​​a cylinder

To understand the above formulas, let's try to calculate the surface area of ​​a cylinder using examples.

1. The radius of the base of the cylinder is 2, the height is 3. Determine the area of ​​the side surface of the cylinder.

The total surface area is calculated by the formula: S side. = 2prh

S side = 2 * 3.14 * 2 * 3

S side = 6.28 * 6

S side = 37.68

The lateral surface area of ​​the cylinder is 37.68.

2. How to find the surface area of ​​a cylinder if the height is 4 and the radius is 6?

The total surface area is calculated by the formula: S = 2πr 2 + 2πrh

S = 2 * 3.14 * 6 2 + 2 * 3.14 * 6 * 4

S = 2 * 3.14 * 36 + 2 * 3.14 * 24

A cylinder is a figure consisting of a cylindrical surface and two circles arranged in parallel. Calculating the area of ​​a cylinder is a problem in the geometric branch of mathematics, which is solved quite simply. There are several methods for solving it, which as a result always come down to one formula.

How to find the area of ​​a cylinder - calculation rules

• To find out the area of ​​\u200b\u200bthe cylinder, you need to add two base areas with the area of ​​\u200b\u200bthe lateral surface: S \u003d S side. + 2 S main. In a more detailed version, this formula looks like this: S= 2 π rh+ 2 π r2= 2 π r(h+ r).
• The area of ​​the lateral surface of a given geometric body can be calculated if its height and the radius of the circle lying at the base are known. In this case, you can express the radius from the circumference, if it is given. The height can be found if the value of the generatrix is ​​specified in the condition. In this case, the generatrix will be equal to the height. The formula for the lateral surface of a given body looks like this: S= 2 π rh.
• The area of ​​the base is calculated according to the formula for finding the area of ​​a circle: S osn= π r 2 . In some problems, the radius may not be given, but the circumference is given. With this formula, the radius is expressed quite easily. С=2π r, r= С/2π. It must also be remembered that the radius is half the diameter.
• When performing all these calculations, the number π is usually not translated into 3.14159 ... You just need to add it next to the numerical value that was obtained as a result of the calculations.
• Further, it is only necessary to multiply the found base area by 2 and add to the resulting number the calculated area of ​​\u200b\u200bthe lateral surface of the figure.
• If the problem indicates that the cylinder has an axial section and this is a rectangle, then the solution will be slightly different. In this case, the width of the rectangle will be the diameter of the circle that lies at the base of the body. The length of the figure will be equal to the generatrix or the height of the cylinder. It is necessary to calculate the desired values ​​​​and substitute in an already known formula. In this case, the width of the rectangle must be divided by two to find the area of ​​the base. To find the side surface, the length is multiplied by two radii and by the number π.
• You can calculate the area of ​​a given geometric body through its volume. To do this, you need to derive the missing value from the formula V=π r 2 h.
• There is nothing difficult in calculating the area of ​​a cylinder. You only need to know the formulas and be able to derive from them the quantities necessary for the calculations.

Cylinder radius formula:
where V is the volume of the cylinder, h is the height

A cylinder is a geometric body that is obtained by rotating a rectangle around its side. Also, a cylinder is a body bounded by a cylindrical surface and two parallel planes intersecting it. This surface is formed when a straight line moves parallel to itself. In this case, the selected point of the straight line moves along a certain flat curve (guide). This straight line is called the generatrix of the cylindrical surface.
Cylinder radius formula:
where Sb - side surface area, h - height

A cylinder is a geometric body that is obtained by rotating a rectangle around its side. Also, a cylinder is a body bounded by a cylindrical surface and two parallel planes intersecting it. This surface is formed when a straight line moves parallel to itself. In this case, the selected point of the straight line moves along a certain flat curve (guide). This straight line is called the generatrix of the cylindrical surface.
Cylinder radius formula:
where S is the total surface area, h is the height