It’s the most wonderful time of the year, so what better way to celebrate than with a little integration? Here’s a barely veiled pure maths question in festive guise!

The outer surface of a (jingle) bell is described by the revolution of the function

about the y axis where is a positive constant.

**Question 1: **Determine the volume of the solid bell in terms of .

The bells are packaged in a snugly fitting cylindrical box of height whose radius is the same as that of the bell’s base.

**Question 2:** Verify that the bell occupies exactly half the volume of the box.

This post comes with an edition to puzzle #7. Take a look before the apocalypse!

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