Volume of revolution — Different upper trig curve

Question

The region between and from to their first intersection is rotated about the -axis. Find the volume.

This practice question was inspired by Question 13(b) in the 2020 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.Intersection: .
Finish the calculation, then check that the result meets the question’s conditions..
State the final answer clearly in the form the question requested..

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

Verification: Identity .

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