Surface Area and Volume: Surface Area and Volume of Pyramids and Cones

Volume of a Pyramid or Cone

To find the volume of either a pyramid or cone, the process is the same.

V = one-third (area of base)(height)

 

Volume:

  1. Decide which surface is the base.
  2. Find the area of this base.
  3. Use the formula to find the volume.
  4. Label the answer 'cubic units'.

Example:
Let’s find the volume of a square pyramid with dimensions of the base L = 8 in and W = 8 in, and height 6 in.

Pyramid with square base
Pyramid

 

1. Decide which surface is the base.

It is clear in this figure, that the square with dimensions L = 8 in and W = 8 in is the base.

2. Find the area of this base.

A = L·W
A = (8)(8)
A = 64

3. Use the formula to find the volume.

V = one-third(area of base)(height)
V = one-third(64)(6)
V = 128

4. Label the answer 'cubic units'.

The volume is 128 in³.