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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(x^2)?

(A) 9(x^2)
(B) 27(x^3)
(C) 81(x^2)
(D) 81(x^3)
(E) 729(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(x^2), each face has area (54(x^2)) over 6 equals 9(x^2). Therefore, each edge has length square root (9(x^2)), or 3x. The volume is (3x)^3, or 27(x^3).