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← 2020 HSC Extension 1 paper Question 13(b)

Variation 3 · answer guide

Volume of revolution — Intersection at π/3

Question

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

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.

Step by step

  1. Set up the solution: identify the radius and use the disk or washer formula with the correct variable and bounds.At , .
  2. Finish the calculation, then check that the result meets the question’s conditions..
  3. 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: Simplify: .

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

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