Question

the volume of this cone is 113.04 cubic inches. what is the height of this cone? round your answer to the nearest hundredth. 3 in h ≈ inches

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\(V = 113.04\)立方英寸，\(r = 3\)英寸，\(\pi\)取\(3.14\)。

Step2: 代入已知值求解\(h\)

将\(V = 113.04\)，\(r = 3\)，\(\pi = 3.14\)代入公式\(V = \frac{1}{3}\pi r^{2}h\)，得到\(113.04=\frac{1}{3}\times3.14\times3^{2}\times h\)。
先计算\(\frac{1}{3}\times3.14\times3^{2}\)：
\(\frac{1}{3}\times3.14\times9 = 3.14\times3=9.42\)。
则方程变为\(113.04 = 9.42h\)，解得\(h=\frac{113.04}{9.42}=12.00\)。

Answer:

\(12.00\)