Question

the volume of this cone is 6,104.16 cubic centimeters. what is the radius of this cone? round your answer to the nearest hundredth. 18 cm r ≈ centimeters

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\(V = 6104.16\)，\(h = 18\)，\(\pi\)取\(3.14\)。

Step2: 代入数据求解\(r^{2}\)

将\(V = 6104.16\)，\(h = 18\)，\(\pi = 3.14\)代入公式\(V = \frac{1}{3}\pi r^{2}h\)，得到\(6104.16=\frac{1}{3}\times3.14\times r^{2}\times18\)。
先计算\(\frac{1}{3}\times3.14\times18 = 18.84\)，则\(6104.16 = 18.84r^{2}\)，那么\(r^{2}=\frac{6104.16}{18.84}=324\)。

Step3: 求解\(r\)

因为\(r^{2}=324\)，所以\(r=\sqrt{324}=18.00\)（\(r\gt0\)，半径不能为负）。

Answer:

\(18.00\)