Question

what is the volume of a sphere with a diameter of 23.5 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Find the radius

The radius \(r\) of a sphere is half of the diameter \(d\). Given \(d = 23.5\) in, then \(r=\frac{d}{2}=\frac{23.5}{2}=11.75\) in.

Step2: Use the volume formula for a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 11.75\) into the formula:

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Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V\approx2161.3125\times3.14159\).

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Rounding to the nearest tenth, \(V\approx6790.0\)

Answer:

\(6790.0\) cubic inches