Kids Math

Finding the Volume and

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} + 2πrh

r = 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}h

This 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
Back to **Kids Math**

Back to **Kids Study**