AMC8 2012

AMC8 2012 · Q21

AMC8 2012 · Q21. It mainly tests Area & perimeter, 3D geometry (volume).

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?

Marla有一个边长为10英尺的大白色立方体。她还有足够覆盖300平方英尺的绿色油漆。Marla使用所有油漆在每个面上创建一个白色的正方形，中心位置，四周有绿色边框。其中一个白色正方形的面积是多少平方英尺？

(A) $5\sqrt{2}$ $5\sqrt{2}$

(B) 10 10

(D) 50 50

(E) $50\sqrt{2}$ $50\sqrt{2}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

If Marla evenly distributes her $300$ square feet of paint between the 6 faces, each face will get $300\div6 = 50$ square feet of paint. The surface area of one of the faces of the cube is $10^2 = 100$ square feet. Therefore, there will be $100-50 = \boxed{\textbf{(D)}\ 50}$ square feet of white on each side.

如果Marla将她的$300$平方英尺油漆均匀分布到6个面上，每个面将得到$300\div6 = 50$平方英尺的油漆。立方体一个面的表面积是$10^2 = 100$平方英尺。因此，每个面上将有$100-50 = \boxed{\textbf{(D)}\ 50}$平方英尺的白色区域。

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