Test 2 Section 2 - #18 (page 457)

The question is basically asking for which answer will be the smallest volume that is BIGGER than the cylinder ("the smallest box that completely contains the cylinder" means "the smallest box that the cylinder could fit inside"). Plug in values for the variables to help start. Let's call d=4 and h=3.

Since the volume of a cylinder is (π)(radius²)(height), the volume would be (π)(2²)(3), which becomes 12π, which equals about 38. Now just see which of the 5 answer choices is the smallest number that is BIGGER than 38. (A) gives us 12, which is too small. (B) gives us 48, which is bigger than 38, so that works. All the other answers end up being bigger than 48, so they're not correct, since the question asks for the smallest box that will hold the cylinder.