A baby pool is shaped like a short, wide cylinder and holds 52 ft3 of water. A medium pool measures 4 times the height and width of the baby pool. How much water will the medium pool hold?

The volume of a cylinder is the area of the base, times the height.

The area of the circular base is, of course, π times the square of its radius.

So the volume of a cylinder, V, is

V = π h r^2

where h is the height and r is the radius.

If we multiply the height by 3, the new height is 3h.

If we multiply the width by 3, that multiplies the radius (which is half the width) by 3 also.

So the new volume would be

π (3h) (3r) ^2 = π (3h) (9r^2) = 27π h r^2

which is 27 times π h r^2, the volume of the smaller pool. But we know that volume is 37 cubic feet.

So the volume of the larger pool is

27 * 37 cubic feet = 999 cubic feet [answer B]

This is an instance of a general rule:

If we multiply ALL the linear dimensions of an object by a factor F,

while keeping the shape the same (often termed "similar" in geometry),

that multiplies the volume by F^3 (the cube of F).

It also multiplies the surface area by F^2.

These rules are very useful, especially when you hit these questions on an exam under time constraints. If you know them, you'll save time you can use to work other questions.