Volume of revolution — Different power and bounds

Question

Find the volume when from to is rotated about the -axis.

This practice question was inspired by Question 12(b) in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: identify the radius and use the disk or washer formula with the correct variable and bounds..
State the final answer clearly in the form the question requested.Answer: .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Same disk method with a different power.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.