Math: 635f54ee

ID: 635f54ee

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Take the time to break down each piece of information and answer the question being asked.

Method 1: A cube is a three-dimensional square, with six surfaces, all equal in area. The surface area, then, is just 6 * area of a single side, and the area of a square is one of those fundamentals of geometry, the measure of the side times itself (since the four sides of a square are the same). Thus, the area of the surface of a single side of the cube is represented by (a/4)^2, which means that each side is a/4. Finally, the perimeter of a square is 4 times a side length, so

4(a/4) = a

The correct answer is (B).

Method 2: There is virtually no way to get to the correct answer without a core knowledge of geometry, a lucky guess notwithstanding. A calculator will probably be of limited utility unless you want to work with numbers. You could start by drawing a square or cube and assigning a value of, say, 1 to each side.

Now, the surface area will be 6(1)^2, or 6, and the perimeter of a single side is 1 * 4, or 4. To relate this to the expression given, note that in 6(a/4)^2, a/4 must be equivalent to 1 so that the two expressions match.

a/4 = 1

a = 4

As noted above, the correct answer will have a perimeter of 4, and since they all use a, the correct answer must be (B). All the other options multiply a by something else, changing the value from 4 to, well, something else.

Method 3: There is no need to explore a third means of solving the question. Either of the two methods above will do.