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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 times (x^2)
(B) 27 times (x^3)
(C) 81 times (x^2)
(D) 81 times (x^3)
(E) 729 times (x^3)

答案和解析

答案：B

解析：

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 times (x^2)) over 6 equals 9 times (x^2). Therefore, each edge has length square root (9 times (x ^2)), or 3 times x. The volume is (3 times x) ^ 3, or 27 times (x^3).