A cube with an edge length of 4 units has the same volume as a square-based pyramid with base edge lengths of 8 units and a height of h units. What is the value of h?

Guest Jun 1, 2020

#1**0 **

First we need to find the volume of the cube, which is 4^{3}, or 64.

The equation for the volume of a pyramid is V=(1/3)Bh, where B is the area of the base and h is the height. So, we need to find B. The equation is B=lw, where l=length and w=width. Since it is a square, they are going to be the same. That means B=8(8), or 64.

What we know:

V=(1/3)Bh

V=64

B=64

Substitute:

64=(1/3)(64)h

Solve:

Divide both side by 64 to get 1=1/3h

Multiply both side by 3 to get 3=h

Your answer is:

h=3

lovelyy.riss Jun 1, 2020