Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
What is the volume of a cube with surface area 54 times (x ^ 2)?
(A) 9 (x ^ 2)
(B) 27 (x^3)
(C) 81 (x ^ 2)
(D) 81 (x ^ 3)
(E) 729 (x ^ 3)
The correct answer is B
Explanation
Every cube has 6 identical square faces. Since the total surface area of this cube is 54 times (x ^ 2), each face has area (54 (x ^ 2)) /6 =9 (x ^2). Therefore, each edge has length square root (9 (x ^2)), or 3 x. The volume is (3 x) ^ 3, or 27 (x ^ 3).