Here’s a question from the May 2006 SAT exam:
19. A container in the shape of a right circular cylinder has an inside base radius of 4 inches and an inside height of 9 inches. This cylinder is completely filled with water. All of the water is then poured into a second right circular cylinder with a larger inside base radius of 9 inches. What must be the minimum inside height, in inches, of the second cylinder.
(A) 4/3
(B) 16/9
(C) 9/4
(D) 4
(E) 6
Don’t worry about the terminology — it’s not important that you know what a right circular cylinder is. It is, however, important to remember that any time you’re asked about a cylinder, you’re most likely being asked about volume. It’s not necessary to even memorize the volume formula since it’s given to you on the reference information portion of the section (right below the directions). However, we at Stylus suggest you memorize the formulas anyway because it will save you the time of flipping back and forth. Cylinder volume is fairly easy to memorize if you already know the formula for the area of a circle. Think of a cylinder as being a circle with the added dimension of height. Thus, the formula for volume of a cylinder is the same as that of a circle, but with height added: V = πr²h.
Since this question appears toward the end of the section, we can bet on needing to do at least two separate calculations. One way the makers of the SAT love to make geometry equations more complex is by asking you to solve one equation and plug that solution into a second (or even a third) equation to solve for a different variable — to plug and plug again. This equation is no different. Eventually, we’ll need to solve for the height of the second cylinder, but before we can do that, we need to solve for the volume of the original cylinder.
Since the first cylinder is completely full, we only need to plug the given numbers into the formula to find the original volume of water: V = π(4)²(9) = π(16)(9). Don’t bother solving this equation yet — doing so won’t give us the answer we’re looking for, and any time you avoid using a calculator to do messy calculations, you save yourself time.
Onto the second equation: If the water is poured into the second cylinder, it needs to have at least the volume of the original cylinder. So we need to use the volume formula once again, this time using the volume from equation 1 and solving for the height of cylinder 2.
V = πr²h
π(16)(9) = π(9)²h
Divide both sides by 9π to get
16 = 9h (see why I told you not to bother with the calculator?) and then divide by 9 again to get
16/9 = h, choice B.