 ### Question 24

This is a geometry question that requires that you understand the concepts of "volume", "cube" and "surface area."

Key Language

Cube = a box where the base of the cube is a square and the the height is equal to the length of one side of the base.

Area = base times height. In the case of a square the area is the length of any one of the sides squared.

Volume of a cube = the area of the base times the height.

When we are dealing with a cube all of the sides are the same length.

Mathematical Solution

We are asked for the total surface area of the cube. This is the sum of the surface area of the six individual squares that make up the cube. Hence, our job is to find the surface area of one of the six individual squares.

Since the volume of the cube is 8 this means that any of the sides cubed will be equal to 8. Hence, the length of any one of the sides of the cube is 2. Since the length of any one of the sides is 2, the surface area of any one of the 6 squares is 2 times 2 = 4.

If the surface area of one of the 6 squares is 4, the surface area of 6 of the squares (which is the surface area of the whole cube) is 6 times 4 = 24. Hence, the correct answer is (C).

Multiple Choice Is Your Friend Solution

At a minimum you should be able to eliminate (A).

(A) can be eliminated by simply realizing that the volume must be different from the surface area. (Remember that we are told that the surface area is 8.)

When you look at the remaining choices it is clear that:

(B) = 16 = 2 times the surface area
(C) = 24 = 3 times the surface area
(D) = 48 = 6 times the surface area
(E) = 64 = 8 times the surface area

In order to range the answer you might ask: Is the surface area likely to be closest to 2, 3, 6 or 8 times its volume? If you look at it this way, you will likely eliminate (D) and (E).

Hence, the worst case guess is probably (B) or (C).

Back to the tutorial. Go to question 25.