AMC10 2003 A

AMC10 2003 A · Q3

AMC10 2003 A · Q3. It mainly tests Fractions, 3D geometry (surface area).

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?

一个实心盒子尺寸为15 cm × 10 cm × 8 cm。从盒子每个角切除一个边长3 cm的立方体，形成一个新实心体。切除的体积占原体积的百分之多少？

(A) 4.5 4.5

(B) 9 9

(D) 18 18

(E) 24 24

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) The total volume of the eight removed cubes is $8 \times 3^3 = 216$ cubic centimeters, and the volume of the original box is $15 \times 10 \times 8 = 1200$ cubic centimeters. Therefore the volume has been reduced by $\left(\frac{216}{1200}\right)(100\%) = 18\%$.

（D）被移除的 8 个小立方体的总体积为 $8 \times 3^3 = 216$ 立方厘米，原来的长方体盒子的体积为 $15 \times 10 \times 8 = 1200$ 立方厘米。因此体积减少了 $\left(\frac{216}{1200}\right)(100\%) = 18\%$。

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