Volumne of a Pyramid

Volumne of a Pyramid

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

Formula

V = (1/3)Bh, V: Volume of a pyramid, B: Base area, h: Height of the pyramid

V = (1/3)Bh

V: Volume of a pyramid
B: Base area
h: Height of the pyramid

This formula can be used in any pyramid.
(not only a regular pyramid)

Example 1

Find the volume of the given pyramid. The sides of the base: 7, 4. Height: 9.

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

So B = 28.

Area of a rectangle

The height of the given pyramid is 9.

B = 28
h = 9

So V = (1/3)⋅28⋅9.

Cancel the denominator 3
and reduce 9 to 3.

28⋅3 = 84

So V = 84.

Example 2

Find the volume of the given pyramid. The perpendicular edges: 8, 9, and 10.

The three right triangle faces are
all perpendicular to each other.

So set one of these faces as the base.

Set the bottom face as the base.

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

So B = (1/2)⋅8⋅9.

Area of a triangle

(1/2)⋅8 = 4

4⋅9 = 36

So B = 36.

The blue edge is perpendicular to the base.

So the blue edge is the height.

So h = 10.

B = 36
h = 10

So V = (1/3)⋅36⋅10.

(1/3)⋅36 = 12

12⋅10 = 120

So V = 120.