Question

a cone has a height of 20 millimeters and a diameter of 17 millimeters. what is its volume? round your answer to the nearest hundredth. cubic millimeters

Explanation:

Step1: 计算圆锥底面半径

已知圆锥直径\(d = 17\)毫米，根据半径\(r=\frac{d}{2}\)，可得\(r=\frac{17}{2}=8.5\)毫米。

Step2: 代入圆锥体积公式计算

圆锥体积公式为\(V=\frac{1}{3}\pi r^{2}h\)，其中\(h = 20\)毫米，\(r = 8.5\)毫米，\(\pi\)取\(3.14\)。
则\(V=\frac{1}{3}\times3.14\times8.5^{2}\times20\)
先计算\(8.5^{2}=72.25\)，再计算\(\frac{1}{3}\times3.14\times72.25\times20\)
\(\frac{1}{3}\times3.14\times72.25\times20=\frac{3.14\times72.25\times20}{3}\)
\(3.14\times72.25\times20 = 3.14\times1445=4545.3\)
\(\frac{4545.3}{3}=1515.1\)

Answer:

\(1515.10\)