Question

一个实心长方体盒子的尺寸为 $15$ 厘米、 $10$ 厘米、 $8$ 厘米。从这个盒子的每个角切去一个边长 $3$ 厘米的立方体，形成一个新的立体。原体积的百分之多少被切去？

A solid box is $15$ cm by $10$ cm by $8$ cm. A new solid is formed by removing a cube $3$ cm on a side from each corner of this box. What percent of the original volume is removed?

$4.5$

$9$

$12$

$18$

$24$

答案：D

知识点：体积百分数正方体

难度评级：1050

解答：

被切去的八个立方体总体积为 $8 \cdot 3^3 = 216$ 立方厘米。

原盒子体积为 $15 \cdot 10 \cdot 8 = 1200$ 立方厘米。

切去的百分比为 $\dfrac{216}{1200} \cdot 100\% = 18\%$ 。

所以正确答案是 D。

The eight removed cubes have total volume $8 \cdot 3^3 = 216$ cubic centimeters.

The original box has volume $15 \cdot 10 \cdot 8 = 1200$ cubic centimeters.

The percent removed is $\dfrac{216}{1200} \cdot 100\% = 18\%.$

Thus, the correct answer is D.

2003 AMC 10A 第 3 题

答案：D

难度评级：1050

解答：

其他年份的第 3 题