# How to Find Surface Area and Volume of a Cylinder

Now you will learn how to calculate the surface area and volume of a cylinder. First we repeat what a cylinder is. A cylinder is a tube where the top and bottom is a circle or an ellipse. In this entry, you will only work with cylinders with circular faces. The top and the bottom are always identical.

## Surface Area

From the figure above you can see that the surface area of a cylinder consists of the area of two circles or ellipses and one rectangle.

Formula

### SurfaceAreaofaCylinder

 $A=2\cdot \pi \cdot {r}^{2}+2\cdot \pi \cdot r\cdot h$

The first term in the formula is the area of the circles, and the second term is the area of the rectangle. The length of the rectangle is the circumference of the circle.

Example 1

Calculate the surface area of a cylinder with height of $\text{}7\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ and a radius of $\text{}4\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$

 $A=2\cdot \pi \cdot {4}^{2}+2\cdot \pi \cdot 4\cdot 7\approx 276.32\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{2}$

Example 2

Calculate the surface area of a cylinder with height that equals $\text{}4\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ and a diameter of $\text{}6\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$

You must first find the radius of the base (bottom face), $r=\frac{6}{2}=3$:

 $A=2\cdot \pi \cdot {3}^{2}+2\cdot \pi \cdot 3\cdot 4\approx 131.88\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{2}$

## Volume

When calculating the volume of a cylinder, multiply the area of the base by the height of the cylinder.

Formula

### VolumeofaCylinder

 $V=\pi \cdot {r}^{2}\cdot h,$

where $r$ is the radius of the base, and $h$ is the height of the cylinder.

Example 3

Calculate the volume of the cylinder with base equal to a circle with radius $\text{}3\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ and a height of $\text{}5\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$

 $V=\pi \cdot {3}^{2}\cdot 5\approx 141.3\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$

Example 4

Calculate the volume of the cylinder with base equal to a circle with radius $\text{}6\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ and a height of $\text{}8\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$

 $V=\pi \cdot {6}^{2}\cdot 8\approx 904.32\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$