AMC 8 2012 Problem 21

AMC8 2012 年第 21 题

立体几何★★★☆☆

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 英尺的大的白色正方体。她同时还有能够粉刷 300 平方英尺的绿漆。 Marla 使用了全部的绿漆，将白色正方体涂成了这样的一个正方体：正方体的每个面的中央都有一个白色正方形，四周被绿边围绕。那么其中一个面上的白色正方形的面积是多少平方英尺？

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

正确答案 · Correct Answer

解析 · Solution

Solution 1

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 = 50 square feet of white on each side.

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