Question

a cone has a volume of 314 cubic centimeters and a height of 12 centimeters. what is its radius?
round your answer to the nearest hundredth.
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\(V = 314\)立方厘米，\(h = 12\)厘米，\(\pi\approx3.14\)。

Step2: 代入已知值求解\(r^{2}\)

将值代入公式\(314=\frac{1}{3}\times3.14\times r^{2}\times12\)，
先计算\(\frac{1}{3}\times3.14\times12 = 12.56\)，则\(314 = 12.56r^{2}\)，
两边同时除以\(12.56\)，得到\(r^{2}=\frac{314}{12.56}=25\)。

Step3: 求解\(r\)

因为\(r^{2}=25\)，所以\(r = \sqrt{25}=5\)（厘米）。

Answer:

\(5\)