Volume of revolution — Disk volume y=x^3

Question

Find the volume generated 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..
Finish the calculation, then check that the result meets the question’s conditions..
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: Forgetting to square is a common error.

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