Volume of revolution — Cap at y=3

Question

Same curves and , rotated about the -axis up to . Find the volume.

This practice question was inspired by Question 13(a) in the 2021 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..
Finish the calculation, then check that the result meets the question’s conditions.Inner: , so .
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: Volume .

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