Question

the volume of this cone is 47.1 cubic meters. what is the height of this cone? round your answer to the nearest hundredth. 3 m h ≈ meters

Explanation:

Step1: 写出圆锥体积公式

圆锥体积公式为\(V=\frac{1}{3}\pi r^{2}h\)，已知\(V = 47.1\)立方米，\(r = 3\)米。

Step2: 代入数据求解\(h\)

将\(V = 47.1\)，\(r = 3\)代入公式\(V=\frac{1}{3}\pi r^{2}h\)，得到\(47.1=\frac{1}{3}\times3.14\times3^{2}\times h\)。
先计算\(\frac{1}{3}\times3.14\times3^{2}\)：
\(\frac{1}{3}\times3.14\times3^{2}=\frac{1}{3}\times3.14\times9 = 9.42\)。
则方程变为\(47.1 = 9.42h\)，解得\(h=\frac{47.1}{9.42}=5.00\)。

Answer:

\(5.00\)