Question

what is the volume of a sphere with a diameter of 57.1 cm, rounded to the nearest tenth of a cubic centimeter?

Explanation:

Step1: Find the radius

Since the diameter \(d = 57.1\) cm, and the radius \(r=\frac{d}{2}\), then \(r=\frac{57.1}{2}=28.55\) cm.

Step2: Use the formula for the volume of a sphere

The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^{3}\).
Substitute \(r = 28.55\) into the formula:
\(V=\frac{4}{3}\pi(28.55)^{3}\).
First, calculate \((28.55)^{3}=28.55\times28.55\times28.55 = 23429.493625\).
Then, \(V=\frac{4}{3}\times\pi\times23429.493625\).
\(V=\frac{93717.9745}{3}\pi\).
\(V = 31239.32483\pi\).
Taking \(\pi\approx3.14159\), we have \(V=31239.32483\times3.14159\approx98162.3\) \(cm^{3}\).

Answer:

\(98162.3\) \(cm^{3}\)