Question

a square pyramid with a base area of 16 square feet and a cube with a side length of 4 feet have equal volumes. what is the height of the pyramid?

Answer 1

The height of pyramid will be 48 feet

Answer 2

Firstly, we need to understand the formula of the volume of a pyramid:

$\frac{1}{3} \times base \: area \times height$
The volume of the cube:
$4 \times 4 \times 4 \: or \: {4}^{3} \\ = 64 {feet}^{3}$
We can then set up a equation:

Let the height be x feet.
64 = 1/3 × 16 × y
y = 64 × 3 × 1/16
y = 12 feet

Therefore,the height of pyramid is 12 feet.

Hope it helps!