Question

a cone has a volume of 1441.26 cubic millimeters and a radius of 9 millimeters. what is its height? round your answer to the nearest hundredth. h ≈ millimeters

Explanation:

Step1: 写出圆锥体积公式

圆锥体积公式为\(V=\frac{1}{3}\pi r^{2}h\)，其中\(V\)是体积，\(r\)是半径，\(h\)是高。

Step2: 代入已知数据求解\(h\)

已知\(V = 1441.26\)立方毫米，\(r = 9\)毫米，\(\pi\)取\(3.14\)，将其代入公式\(V=\frac{1}{3}\pi r^{2}h\)可得：
\(1441.26=\frac{1}{3}\times3.14\times9^{2}\times h\)
先计算\(\frac{1}{3}\times3.14\times9^{2}\)：
\(\frac{1}{3}\times3.14\times81 = 3.14\times27=84.78\)
则\(1441.26 = 84.78h\)，那么\(h=\frac{1441.26}{84.78}\)。

Step3: 计算\(h\)的值

\(h=\frac{1441.26}{84.78}=17.00\)（毫米）

Answer:

\(17.00\)