AMC8 2025

AMC8 2025 · Q8

AMC8 2025 · Q8. It mainly tests Area & perimeter, 3D geometry (volume).

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 将一个纸板立方体沿一些边切割开来，形成右侧所示的平面形状，其面积为 $18$ 平方厘米。这个立方体的体积是多少立方厘米？

(A) 3\sqrt{3} 3\sqrt{3}

(B) 6 6

(D) 6\sqrt{3} 6\sqrt{3}

(E) 9\sqrt{3} 9\sqrt{3}

Answer

Correct choice: (A)

正确答案：（A）

Solution

Each of the $6$ faces of the cube have equal area, so the area of each face is equal to $\frac{18}{6} = 3$, making the side length $\sqrt3$. From this, we can see that the volume of the cube is $\sqrt{3}^3 = \boxed{\textbf{(A)}~3\sqrt{3}}$

立方体的 $6$ 个面面积相等，因此每个面的面积是 $\frac{18}{6} = 3$，边长为 $\sqrt{3}$。由此，立方体的体积是 $\sqrt{3}^3 = \boxed{\textbf{(A)}~3\sqrt{3}}$。

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