### Home > APCALC > Chapter 1 > Lesson 1.2.1 > Problem 1-23

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