2012 AMC 8 Problems/Problem 21

Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?

$\textbf{(A)}\hspace{.05in}5\sqrt2\qquad\textbf{(B)}\hspace{.05in}10\qquad\textbf{(C)}\hspace{.05in}10\sqrt2\qquad\textbf{(D)}\hspace{.05in}50\qquad\textbf{(E)}\hspace{.05in}50\sqrt2$

Solution

The surface area of this cube is $600$ square feet. Maria's paint can cover a total of $300$ square feet. Since all the faces of the cube have an identical design, Maria's paint covers half of every face of the cube. The surface area of one of the faces of the cube is $100$ square feet. Then, her paint will cover $50$ square feet of every face. Thus, the area of one of the white squares will be $100 - 50 = \boxed{\textbf{(D)}\ 50}$ square feet.

2012 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 20	Followed by Problem 22
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2012 AMC 8 Problems/Problem 21

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