Question

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

Explanation:

Step1: Recall volume - of - sphere formula

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius of the sphere.

Step2: Identify the radius

From the figure, the radius of the semi - circle $r = 4$.

Step3: Calculate the volume of the solid

When a semi - circle is rotated about its diameter, the solid generated is a sphere. Substitute $r = 4$ into the volume formula of a sphere:
$V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(4)^{3}=\frac{4}{3}\pi\times64=\frac{256\pi}{3}\approx268.1$

Answer:

$268.1$