Question

Marla 有一个边长 $10$ 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 用完所有油漆，在每个面上画出一个居中的白色正方形，周围是绿色边框。每个白色正方形的面积是多少平方英尺？

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?

$5\sqrt2$

$10$

$10\sqrt2$

$50$

$50\sqrt2$

答案：D

知识点：表面积正方体

难度评级：1070

小提示：

绿色油漆覆盖了立方体表面积的一半。

The green paint covers half of the cube surface area.

大提示：

剩余未涂区域平均分布在六个面上。

The remaining unpainted area is split equally among the six faces.

视频讲解：

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文字解答：

立方体总表面积为 $6\cdot 10\cdot 10 = 600$ 。因此未被绿色覆盖的面积为 $600-300 = 300$ 平方英尺，平均到每个面是 $\dfrac{300}{6} = 50$ 平方英尺。

所以正确答案是 D。

The total surface area is $6\cdot 10\cdot 10 = 600.$ Therefore, $600-300 = 300$ square feet aren’t covered. This would be $\dfrac{300}{6} = 50$ square feet per face.

Thus, the answer is D .

2012 AMC 8 第 21 题