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?
+12 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
