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The shaded region at right represents a flag (the upper boundary is a semi-circle). Calculate the volume of the solid formed when the flag is rotated about the pole. In a complete sentence, describe the rotated shape. To help you visualize this, use the

It's a sphere on the outside with two cones removed from the inside.

The radius of the sphere is . The radius and height of each cone is also .

Use the eTool below to visualize the flag.
Click the link at right for the full version of the eTool: Calc 2-8 HW eTool

Horizontal segment, with semicircle above, with it's diameter on the right 2 thirds of the segment, with segments connecting the left endpoint of diameter, the highest point of the semicircle, the right endpoint of diameter, & the center of the diameter, creating 2 right triangles, semicircle area outside the triangle is shaded, & vertical segment is labeled 3.