Question

a sphere has a diameter of 10 in. what is the volume of the sphere?

$v = \frac{500}{3}\pi \text{ in}^3$

$v = \frac{125}{3} \text{ in}^3$

$v = \frac{500}{3} \text{ in}^3$

$v = \frac{4000}{3}\pi \text{ in}^3$

Explanation:

Step1: Find the radius

The radius \(r\) of a sphere is half of its diameter. Given diameter \(d = 10\) in, so \(r=\frac{d}{2}=\frac{10}{2}=5\) in.

Step2: Use the volume formula for a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 5\) into the formula:

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Answer:

\(V=\frac{500}{3}\pi\text{ in}^3\) (the first option)