Question

The cube below has sides of length 4 feet. If a cylindrical section of radius 2 feet is removed from the solid, what is the total remaining volume of the cube? Express your answer in cubic feet in terms of pi.

Answer 1

Because the main shape is a cube and a cube has all sides equal in length, the volume (l*w*h) is 4*4*4=64. No pi in that volume. Just 64 ft^3. The volume for a cylinder is
`V= \pi r^2h`. The radius is 2 feet and the height is the same as the height of the cube from which it was removed. So volume for the cylinder is
`V= \pi (2)^24` which is
`16 \pi`. Since we are removing the volume of the cylinder from the volume of the cube, the volume remaining, in terms of pi is
`64-16 \pi ft^3`