The surface area of a cube is , where a is a positive constant. Which of the following gives the

Question

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?

Accepted Answer

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 4 a , 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 6 a , then the total surface area of the cube is , which is not .

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