2003 AMC 10A 第 3 题

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

每个被切去的立方体体积是

3^3

。

Each removed cube has volume

3^3

有

8

个角，原长方体体积为

15 \cdot 10 \cdot 8

。

There are

8

corners, and the original volume is

15 \cdot 10 \cdot 8

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.

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