Question

find the volume of this cone.
round to the nearest tenth.
10ft
6ft
? ft³
submit

Explanation:

Step1: Find the height of the cone

Using the Pythagorean theorem \(h=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64} = 8\) ft.

Step2: Use the volume formula for a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Here \(r = 6\) ft and \(h=8\) ft.
Substitute the values: \(V=\frac{1}{3}\times\pi\times6^{2}\times8\).
First calculate \(6^{2}=36\), then \(V=\frac{1}{3}\times\pi\times36\times8\).
\(\frac{1}{3}\times36 = 12\), so \(V=12\times\pi\times8=96\pi\).
Using \(\pi\approx3.14\), \(V\approx96\times3.14 = 301.44\approx301.4\) \(ft^{3}\).

Answer:

\(301.4\)