Question

Find the height in centimeters of a square pyramid with a volume of 72cm^ 3 and a base edge length equal to the height

Answer 1

The height of the pyramid is 6 cm.

Explanation:

The volume of a square pyramid is given by:

`V = (1)/(3)A_(b)h = 72 cm^(3)`

Where:

`A_(b)`: is the area of the base

h: is the height

Since the base edge length is equal to the height, the area of the base is:

`A_(b) = l^(2) = h^(2)`

Hence, the height is:

`72 cm^(3) = (1)/(3)A_(b)h = (1)/(3)h^(2)h`

`h = (3*72 cm^(3))^(1/3) = 6 cm`

Therefore, the height of the pyramid is 6 cm.

I hope it helps you!