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3-181.

Calculate the volume of the solid created when the semi-circular flag at right is rotated about the pole. Describe the rotated solid. Homework Help ✎

This flag will look like a sphere with a cylindrical hole removed from its center.

volume = sphere − cylinder

Use the Pythagorean Theorem to compute the radius of the sphere.

Semi-circle on top of a horizontal flagpole. The diameter is resting on the pole.  Inscribed within the semicircle is an 8 by 6 rectangle. The 6 side is perpendicular with the pole.  The 8 side is parallel to the pole.