Question

what is the volume of this cone?
round your answer to the nearest hundredth.
20 m
34 m
cubic meters
submit

Explanation:

Step1: Find the radius

The diameter is \(34\) m, so the radius \(r=\frac{34}{2}=17\) m.

Step2: Find the height

Use the Pythagorean theorem \(h = \sqrt{l^{2}-r^{2}}\), where \(l = 20\) m (slant height).
\(h=\sqrt{20^{2}-17^{2}}=\sqrt{400 - 289}=\sqrt{111}\approx10.5357\) m.

Step3: Calculate the volume

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\).
Substitute \(r = 17\) and \(h\approx10.5357\):
\(V=\frac{1}{3}\times\pi\times17^{2}\times10.5357\)
\(V=\frac{1}{3}\times\pi\times289\times10.5357\)
\(V=\frac{1}{3}\times\pi\times3044.8173\)
\(V\approx\frac{3044.8173\times3.1416}{3}\)
\(V\approx\frac{9565.39}{3}\approx3188.46\)

Answer:

\(3188.46\)