Pyramid: Volume

How to find the volume of a pyramid: formula, 2 examples, and their solutions.

Formula

Formula

V = [1/3]Bh

V: Volume of a cone
B: Base area
h: Height

The pyramid doesn't have to be
a regular pyramid.

Example 1

Example

Solution

Find the base area B.

The base is a rectangle.
Its sides are 7 and 4.

So the area of the rectangle is
B = 7⋅4.

7⋅4 = 28.

So the base area B is 28.

The height h is 9.

B = 28
h = 9

Then the volume V
is equal to
1/3
times,
the base area, 28
times,
the height h, 9.

[1/3]⋅9 = 3

28⋅3 = 84

So the volume of the pyramid is 84.

Example 2

Example

Solution

Find the base area B.

The base is a right triangle.
Its legs are 8 and 9.

So the area of the triangle is
B = [1/2]⋅8⋅9.

You can also choose the other triangles
as the base.
You'll get the same answer.

[1/2]⋅8 = 4

4⋅9 = 36

So the base area B is 36.

The height h is 10.

B = 36
h = 10

Then the volume V
is equal to
1/3
times,
the base area, 36
times,
the height h, 10.

[1/3]⋅36 = 12

12⋅10 = 120

So the volume of the pyramid is 120.