Question

what is the volume of this sphere?
round your answer to the nearest hundredth.
40 mm
cubic millimeters

Explanation:

Step1: Find the radius

Given the diameter \(d = 40\) mm, the radius \(r=\frac{d}{2}\).
\(r=\frac{40}{2}=20\) mm.

Step2: Use the volume formula for a sphere

The volume formula for a sphere is \(V = \frac{4}{3}\pi r^{3}\).
Substitute \(r = 20\) into the formula:
\(V=\frac{4}{3}\pi(20)^{3}\).
First, calculate \((20)^{3}=20\times20\times20 = 8000\).
Then \(V=\frac{4}{3}\pi\times8000=\frac{32000\pi}{3}\).
Using \(\pi\approx3.14159\), \(V=\frac{32000\times3.14159}{3}\).
\(32000\times3.14159 = 100530.88\).
\(V=\frac{100530.88}{3}\approx33510.29\) (rounded to the nearest hundredth).

Answer:

\(33510.29\)