Rates of change — Different volume rate

Question

If and , find in terms of .

This practice question was inspired by Question 11(f) 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: write the geometric constraint, differentiate every changing quantity with respect to time, then substitute..
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 method, new constant rate.

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