Question

一个立方体的表面积是体积为 $1$ 的立方体表面积的两倍。这个立方体的体积是多少？

What is the volume of a cube whose surface area is twice that of a cube with volume $1?$

$\sqrt{2}$

$2$

$2\sqrt{2}$

$4$

$8$

答案：C

知识点：正方体表面积体积

难度评级：1380

解答：

体积为 $1$ 的立方体边长为 $1$ ，表面积为 $6$ 。所求立方体表面积为 $12$ 。若边长为 $s$ ，则 $6s^2 = 12$ ，所以 $s = \sqrt{2}$ 。

其体积为 $(\sqrt{2})^3 = 2\sqrt{2}.$

所以正确答案是 C。

The cube with volume $1$ has side $1$ and surface area $6.$ The larger cube has surface area $12,$ so if its side is $s,$ then $6s^2 = 12,$ giving $s = \sqrt{2}.$

Its volume is $(\sqrt{2})^3 = 2\sqrt{2}.$

Thus, C is the correct answer.

2008 AMC 12A 第 8 题

答案：C

难度评级：1380

解答：

其他年份的第 8 题