AMC8 2008

AMC8 2008 · Q21

AMC8 2008 · Q21. It mainly tests Area & perimeter, 3D geometry (volume).

Jerry cuts a wedge from a $6$-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?

杰瑞从一个6厘米高的博洛尼亚香肠圆柱体中切下一个楔形块，如虚线所示。哪个选项最接近他的楔形块的体积（立方厘米）？

(A) 48 48

(B) 75 75

(D) 192 192

(E) 603 603

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Using the formula for the volume of a cylinder, the bologna has volume $ \pi r^2 h = \pi \times 4^2 \times 6 = 96\pi $. The cut divides the bologna in half. The half-cylinder will have volume $ \frac{96\pi}{2} = 48\pi \approx 151\ \text{cm}^3 $. Note: The value of $\pi$ is slightly greater than 3, so to estimate the volume multiply $48(3)=144\ \text{cm}^3$. The product is slightly less than and closer to answer C than any other answer.

答案（C）：使用圆柱体体积公式，这块博洛尼亚香肠的体积为 $ \pi r^2 h = \pi \times 4^2 \times 6 = 96\pi $。切一刀把香肠分成两半。半圆柱的体积为 $ \frac{96\pi}{2} = 48\pi \approx 151\ \text{cm}^3 $。注：$\pi$ 的值略大于 3，因此估算体积时可用 $48(3)=144\ \text{cm}^3$。该结果略小于真实值，并且比其他选项更接近答案 C。

Topics