Question

what is the volume of a sphere with a diameter of 7.9 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Find the radius

Since the diameter \(d = 7.9\) ft, and the radius \(r=\frac{d}{2}\), then \(r=\frac{7.9}{2}=3.95\) ft.

Step2: Use the volume formula for a sphere

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 3.95\) into the formula:
\(V=\frac{4}{3}\pi(3.95)^{3}\)
First, calculate \((3.95)^{3}=3.95\times3.95\times3.95 = 61.629875\)
Then, \(V=\frac{4}{3}\pi\times61.629875\)
\(V=\frac{246.5195\pi}{3}\)
Using \(\pi\approx3.14159\), we have \(V=\frac{246.5195\times3.14159}{3}\)
\(246.5195\times3.14159 = 774.5797\)
\(V=\frac{774.5797}{3}=258.1932\approx258.2\)

Answer:

\(258.2\) cubic feet