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 $h$?
To solve this problem, I need to find the volume of the cube and the volume of the pyramid, and set them equal to each other. The volume of a cube is given by the formula $V = s^3$, where $s$ is the edge length. So, the volume of the cube in this problem is $V = 4^3 = 64$ cubic units. The volume of a pyramid is given by the formula $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. So, the volume of the pyramid in this problem is $V = \frac{1}{3}(8^2)h = \frac{64}{3}h$ cubic units. Now, I can set the volumes equal to each other and solve for $h$. I get $64 = \frac{64}{3}h$, which implies that $h = 3$ units. 