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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?

 Jun 1, 2020
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First we need to find the volume of the cube, which is 43, 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

 Jun 1, 2020
edited by lovelyy.riss  Jun 1, 2020
edited by lovelyy.riss  Jun 1, 2020

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