AMC 8 2025 Problem 8
AMC8 2025 年第 8 题
立体几何★★☆☆☆
Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area of 18 square centimeters. What is the volume of the cube in cubic centimeters?
Isaiah沿着一个硬纸板立方体的部分边缘将其剪开，形成右下图所示的平面图形，该图形的面积为18平方厘米。请问这个立方体的体积是多少立方厘米？
- A.
- B.6
- C.9
- D.
- E.
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
Each of the 6 faces of the cube have equal area, so the area of each face is equal to , making the side length . From this, we can see that the volume of the cube is .
Let the side length of the cube shown be equal to centimeters. The surface area of this cube is equal to the area of the net of the cube, which is equal to 18 square centimeters. The surface area of this cube is also square centimeters, so we have However, we aren't done. We have found that the side length of the cube is cm, but the question asks for the volume of the cube, which is equal to cubic centimeters.
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