Question

find the volume of the cone. round your answer to the nearest tenth

the volume of the cone is about □ cubic feet

Explanation:

Step1: Recall the formula for the volume of a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 4\) ft and \(h=\sqrt{7^{2}-4^{2}}=\sqrt{49 - 16}=\sqrt{33}\approx5.7\) ft.
\(V=\frac{1}{3}\times\pi\times4^{2}\times5.7\)
\(V=\frac{1}{3}\times\pi\times16\times5.7\)
\(V=\frac{91.2\pi}{3}\)
\(V = 30.4\pi\)

Step3: Calculate the value

\(V\approx30.4\times3.14 = 95.456\approx95.5\)

Answer:

\(95.5\)