Question

the volume of this cone is 2,863.68 cubic feet. what is the radius of this cone? round your answer to the nearest hundredth. 19 ft r ≈ feet

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\(V = 2863.68\)立方英尺，\(h=19\)英尺，\(\pi\)取\(3.14\)。

Step2: 代入已知值求解\(r^{2}\)

将\(V = 2863.68\)，\(h = 19\)，\(\pi=3.14\)代入公式\(V=\frac{1}{3}\pi r^{2}h\)，得到\(2863.68=\frac{1}{3}\times3.14\times r^{2}\times19\)。
先计算\(\frac{1}{3}\times3.14\times19\)：
\(\frac{1}{3}\times3.14\times19=\frac{3.14\times19}{3}=\frac{59.66}{3}\approx19.89\)。
则\(2863.68 = 19.89r^{2}\)，所以\(r^{2}=\frac{2863.68}{19.89}=144\)。

Step3: 求解\(r\)

因为\(r^{2}=144\)，所以\(r=\sqrt{144}=12.00\)（英尺）。

Answer:

\(12.00\)