Question

what is the volume of this cone?
round your answer to the nearest hundredth.
17 m
26 m
cubic meters
submit
work it out
not feeling ready yet? these can help:
area of circles
lesson: volume of cones

Explanation:

Step1: 求圆锥底面半径

已知圆锥底面直径\(d = 26m\)，根据半径\(r=\frac{d}{2}\)，可得\(r=\frac{26}{2}=13m\)。

Step2: 求圆锥的高

根据勾股定理\(h=\sqrt{l^{2}-r^{2}}\)（\(l\)为圆锥母线长，\(l = 17m\)），则\(h=\sqrt{17^{2}-13^{2}}=\sqrt{(17 + 13)\times(17 - 13)}=\sqrt{30\times4}=\sqrt{120}=2\sqrt{30}\approx 10.95m\)。

Step3: 计算圆锥体积

圆锥体积公式\(V=\frac{1}{3}\pi r^{2}h\)，将\(r = 13\)，\(h\approx10.95\)代入，\(V=\frac{1}{3}\times\pi\times13^{2}\times10.95\approx\frac{1}{3}\times3.14\times169\times10.95\)。
先计算\(169\times10.95 = 1850.55\)，再计算\(\frac{1}{3}\times3.14\times1850.55=3.14\times616.85 = 1937.90\)（\(m^{3}\)）。

Answer:

\(1937.90\)