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 1-23 HW eTool (Desmos).
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.
Calculate 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