Problem

A filled semicircular region of radius \(r\) rotates \(360°\) about its diameter. Use the diagram to state the generating region, axis, resulting solid, radius, and volume.

Prompt diagram for M3-037-A11-V03: the generating region, rotation axis, dimensions, and 360-degree sweep with the resulting solid withheld.

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The generating region is treated as only its semicircular boundary, the axis is its diameter, the result is a hollow spherical surface of radius r, and its enclosed volume is 0.

The generating region is the filled semicircle, the axis is its diameter, the solid is a cylinder of radius r and height 2r, and its volume is 2pi r³.

The generating region is the filled semicircle, the axis is its diameter, the solid is a hemisphere of radius r, and its volume is (2/3)pi r³.

The generating region is the filled semicircle, the axis is its diameter, the solid is a sphere of radius r, and its volume is (4/3)pi r³.

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A filled semicircular region of radius \(r\) rotates \(360°\) about its diameter. Use the diagram to state the generating region, axis, resulting solid, radius, and volume.

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