# Kids Math

## Finding the Volume and

Surface Area of a Cylinder

Surface Area of a Cylinder

**What is a cylinder?**

There are different kinds of cylinders. On this page we will be discussing the most simple form where the cylinder looks like a tube or a soup can with two circles at each end that are the same size and parallel.

**Terms of a Cylinder**

In order to calculate the surface area and volume of a cylinder we first need to understand a few terms:

Radius - The radius is the distance from the center to the edge of the circles at each end.

Pi - Pi is a special number used with circles. We will use an abbreviated version where Pi = 3.14. We also use the symbol π to refer to the number pi in formulas.

Height - The height or length of the cylinder.

**Surface Area of a Cylinder**

The surface area of a cylinder is the surface area of both circles at each end plus the surface area of the outside of the tube. There is a special formula used to figure this out.

Surface area = 2πr

^{2}+ 2πrhr = radius

h = height

π = 3.14

This is the same as saying (2 x 3.14 x radius x radius) + (2 x 3.14 x radius x height)

Example:

What is the surface area of a cylinder with radius 3 cm and height 5 cm?

Surface area = 2πr

^{2}+ 2πrh

= (2x3.14x3x3) + (2x3.14x3x5)

= 56.52 + 94.2

= 150.72 cm

^{2}

**Volume of a Cylinder**

There is special formula for finding the volume of a cylinder. The volume is how much space takes up the inside of a cylinder. The answer to a volume question is always in cubic units.

Volume = πr

^{2}hThis is the same as 3.14 x radius x radius x height

Example:

Find the volume of a cylinder with radius 3 cm and height 5 cm?

Volume = πr

^{2}h

= 3.14 x 3 x 3 x 5

= 141.3 cm

^{3}

**Things to Remember**

- Surface area of a cylinder = 2πr
^{2}+ 2πrh - Volume of a cylinder = πr
^{2}h - You need to know the radius and height to figure both the volume and surface area of a cylinder.
- Answers for volume problems should always be in cubic units.
- Answers for surface area problems should always be in square units.

**More Geometry Subjects**

Circle

Polygons

Quadrilaterals

Triangles

Pythagorean Theorem

Perimeter

Slope

Surface Area

Volume of a Box or Cube

Volume and Surface Area of a Sphere

Volume and Surface Area of a Cylinder

Volume and Surface Area of a Cone

Angles glossary

Figures and Shapes glossary

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