The surface area of a cube is , where a is a positive constant. Which of the following gives the perimeter of one face of the cube?
A
B
C
D
Correct answer: B
Explanation
Choice B is correct. A cube has 6 faces of equal area, so if the total surface area of a cube is , then the area of one face is . Likewise, the area of one face of a cube is the square of one of its edges; therefore, if the area of one face is , then the length of one edge of the cube is . Since the perimeter of one face of a cube is four times the length of one edge, the perimeter is .
Choice A is incorrect because if the perimeter of one face of the cube is , then the total surface area of the cube is , which is not . Choice C is incorrect because if the perimeter of one face of the cube is 4a, then the total surface area of the cube is , which is not . Choice D is incorrect because if the perimeter of one face of the cube is 6a, then the total surface area of the cube is , which is not .
SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.
id cb_question_bank:a666adb0-1d55-48c9-bf7d-f6c7bf70c537 · question 635f54ee · IBN 05720-DC
· JSON