# Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in. The second pyramid has a height of 84 in. What is the side length of the base of the second pyramid?

**Solution:**

The volume of a square pyramid = 1/3a^{2}h

Where a is the base length

h is the height

Side length of base = 20 inches

Height = 21 inches

Substituting it in the formula

Volume of first pyramid = 1/3 × 20^{2} × 21

By further calculation

= 1/3 × 400 × 21

= 2800 inches^{3}

As volume of both the equations is same

V = 2800 inches^{3}

a = ?

h = 84 inches

Substituting it in the formula

2800 = 1/3 × a^{2} × 84

So we get

a^{2} = [2800 × 3]/ 84

a^{2} = 100

a = 10 inches

Therefore, the side length of the base of the second pyramid is 10 inches.

## Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in. The second pyramid has a height of 84 in. What is the side length of the base of the second pyramid?

**Summary:**

Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in. The second pyramid has a height of 84 in. The side length of the base of the second pyramid is 10 inches.