Question

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?

Answer 1

The volume of the pyramid for a square base can be written as: 

V = $\frac{ s^{2}H }{3}$

First, get the volume of the first pyramid
V = ?
s = 20 in.
H = 21 in.

V = $\frac{ 20^{2}(21)}{3}$
V = 2800 in³

Since, the volume of two pyramids are the same, we will equate it to equation 2 

V = 2800 in³
s = ?
H = 84 in.

Applying it to the formula:
2800 = $\frac{ s^{2}(84)}{3}$
$\frac{(2800)(3)}{84}$ = s²    ⇒ combine like terms 
100 = s²        ⇒ get the square root of both sides to get the value of s
10 in = s       ⇒side length of the base of the second pyramid