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 = 2πr2 + 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 = 2πr2 + 2πrh
= (2×3.14x3x3) + (2×3.14x3x5)
= 56.52 + 94.2
= 150.72 cm2
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 = πr2h
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 = πr2h
= 3.14 x 3 x 3 x 5
= 141.3 cm 3
Things to Remember
- Surface area of a cylinder = 2πr2 + 2πrh
- Volume of a cylinder = πr2h
- 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.