# Video: US-SAT05S4-Q10-287125359841

The surface area of a cube is 6(π/2)Β², where π is a positive constant. Which of the following gives the perimeter of one face of the cube? [A] 2π [B] 6π [C] π [D] π/2

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### Video Transcript

The surface area of a cube is six times π over two squared, where π is a positive constant. Which of the following gives the perimeter of one face of the cube? A) two π, B) six π, C) π, or D) π over two.

If we think about a cube, itβs made of six faces, all of which are squares. And if the surface area of a cube is six times π over two squared, then π over two squared is the area of each face of our cube, the area of a square. And we know that the area of a square equals side squared. And for us, π over two squared is the area. π over two squared equals side squared, where π  is the length of one of the sides of the square.

And we know that all four of the sides are the same length. If π over two squared equals the area, then π , the side length, is just π over two. And if one side measures π over two, then the perimeter of our square is four times that side. The perimeter is four times π over two. The four over two reduces to two. And we can say that the perimeter is two π. This makes sense because if we add π over two plus π over two, that would be equal to π.

The other two sides are also equal to π over two. When we add those two sides together, we get π. And that means all four sides together would be two π, which is option A.