Question

the volume of this cone is 1,256 cubic meters. what is the radius of this cone? round your answer to the nearest hundredth. 12 m r ≈ meters submit work it out not feeling ready yet? these can help: area of circles lesson: volume of cones

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\(V = 1256\)立方米，\(h = 12\)米。

Step2: 代入已知值求解\(r^{2}\)

将\(V = 1256\)，\(h = 12\)代入公式\(1256=\frac{1}{3}\times\pi\times r^{2}\times12\)，先化简等式右边\(\frac{1}{3}\times12 = 4\)，得到\(1256 = 4\pi r^{2}\)，则\(r^{2}=\frac{1256}{4\pi}\)。

Step3: 计算\(r^{2}\)的值

取\(\pi\approx3.14\)，\(r^{2}=\frac{1256}{4\times3.14}=\frac{1256}{12.56} = 100\)。

Step4: 求解\(r\)

因为\(r^{2}=100\)，所以\(r=\sqrt{100}= 10.00\)（米）。

Answer:

\(10.00\)