91Ó°ÊÓ

The street department's storage building, which is used to store the rock, gravel, and salt used on the city's roadways, is built in the shape of a regular hexagonal pyramid. The altitude of the pyramid has the same length as any side of the base. If the volume of the interior is \(11,972 \mathrm{ft}^{3},\) find the length of the altitude and of each side of the base to the nearest foot.

The numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?

Suppose that a semicircular region with a vertical diameter of length 4 is rotated about that diameter. Determine the exact surface area and the exact volume of the resulting solid of revolution.