Question

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

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume 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 diagram, the radius \(r = 6\) units.

Step3: Calculate the volume of the sphere

Substitute \(r = 6\) into the formula:

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Using \(\pi\approx3.14\), we get \(V = 288\times3.14=904.32\approx904.3\) (rounded to the nearest tenth)

Answer:

\(904.3\) units³