Question

question
find the volume of the solid generated when the semicircle below is rotated about its diameter,
uvw. round your answer to the nearest tenth if necessary.
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Explanation:

Step1: Recall the formula for the volume of a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\). When a semicircle is rotated about its diameter, it forms a sphere.

Step2: Identify the radius

From the figure, the radius \(r = 2\).

Step3: Substitute the radius into the formula

Substitute \(r = 2\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi\times(2)^{3}\).

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Answer:

\(33.5\)