Question

the volume of this cone is 37.68 cubic centimeters. what is the radius of this cone?
round your answer to the nearest hundredth.
4 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\(V = 37.68\)立方厘米，\(h=4\)厘米，\(\pi\)取\(3.14\)。

Step2: 代入数据求解\(r^{2}\)

将\(V = 37.68\)，\(h = 4\)，\(\pi=3.14\)代入公式\(V=\frac{1}{3}\pi r^{2}h\)，得到\(37.68=\frac{1}{3}\times3.14\times r^{2}\times4\)。
先计算\(\frac{1}{3}\times3.14\times4=\frac{12.56}{3}\)，则\(37.68=\frac{12.56}{3}r^{2}\)，\(r^{2}=37.68\div\frac{12.56}{3}\)，\(r^{2}=37.68\times\frac{3}{12.56}\)，\(r^{2}=9\)。

Step3: 求解\(r\)

因为\(r^{2}=9\)，所以\(r = 3.00\)（厘米）（\(r>0\)，舍去\(r=- 3\)）。

Answer:

\(3.00\)