Curved Solids Lab

Four ways to use it in class

1. Before you write 2πrh on the board, unroll the cylinder. Ask how wide the rectangle has to be for the paper to meet — the class will tell you it is the circumference.
2. Unroll the cone. The curved edge has to be as long as the base circle, so the sector's angle is 2πr ÷ l. That sentence is the whole of πrl.
3. Slide the radius up on the cone and watch the sector's angle open. Ask what shape of cone would need a whole circle of paper — nothing does, and asking why is a good five minutes.
4. Pour the cone into its cylinder and count aloud. Then the sphere, and point out that its cylinder is a different one: the one it just fits inside.