Question

find the volume of the cone. round your answer to the nearest tenth.
the volume of the cone is about
9
cubic yards

Explanation:

Step1: Find the height of the cone

Use the Pythagorean theorem \(h=\sqrt{l^{2}-r^{2}}\). Given \(l = 9\) yd and \(r=7\) yd.
\(h=\sqrt{9^{2}-7^{2}}=\sqrt{81 - 49}=\sqrt{32}\approx5.7\) yd

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(r = 7\) yd and \(h\approx5.7\) yd.
\(V=\frac{1}{3}\times\pi\times7^{2}\times5.7=\frac{1}{3}\times\pi\times49\times5.7\)
\(V=\frac{1}{3}\times\pi\times279.3\)
\(V = 93.1\pi\approx93.1\times3.14 = 292.3\)

Answer:

\(292.3\)