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

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
`(1)/(3) {a}^(2)h`

Given a = 5 inches , h = height of pyramid

`= > (1)/(3) {a}^(2) h`

`= > (1)/(3)(5)^(2)h`

`= > (1)/(3) * 25 * h`

`= > (25)/(3)h`

then,

`125 = (25h)/(3)`

`= > 25h = 125 * 3`

`= > 25h = 375`

`= > h = (375)/(25)`

`= > h = 15`

Hence, the height of pyramid is 15 inches