Question

A cube with sides 5 inches, and a pyramid with base edges 5 inches. What is the height, so that the volume of the cube and the pyramid are equal?

Answer 1

15 inches is the height of the pyramid

Step-by-step explanation:

The volume of a cube is a³

Given a = 5 inches

→ Volume = a³

= 5³

= 5×5×5

= 125 in²

The volume of a pyramid is $\frac{1}{3} {a}^{2}h$

Given a = 5 inches , h = height of pyramid

$= > \frac{1}{3} {a}^{2} h$

$= > \frac{1}{3}(5)^{2}h$

$= > \frac{1}{3} \times 25 \times h$

$= > \frac{25}{3}h$

then,

$125 = \frac{25h}{3}$

$= > 25h = 125 \times 3$

$= > 25h = 375$

$= > h = \frac{375}{25}$

$= > h = 15$

Hence, the height of pyramid is 15 inches