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A semi-circular flag is shown attached to a "pole" at right.

  1. Imagine rotating the flag about its pole and describe the resulting three-dimensional figure. Draw a picture of this figure on your paper.
    To help you visualize this, use the .

    You can build a model of a rotating flag problem. All you need is a pencil, scissors, tape and some paper. To build your model, cut out a flag and tape it to a pencil (which represents the flagpole). Once assembled, spin the pencil rapidly between your hands. If you spin the pencil fast enough, you will see a 3D figure. In this case, it will be a sphere.

  2. Find the volume of the rotated flag.

    Be careful! The radius of this sphere is not .

Use the eTool below to visualize the flag.
Click the link at right for the full version of the eTool: Calc 1-23 HW eTool