Practice variation 2 of 3
Rates of change — Tank with rate constant $m$
Your question
Hemispherical bowl radius , volume , and while water flows in and out.
(i) Derive .
(ii) Hence show the fill time from empty to full is .
(iii) Inflow then stops; draining alone satisfies . Show the empty time is .
This practice question was inspired by Question 13(a) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?