Practice variation 3 of 3
Rates of change — Parallel hemispherical tank chain
Your question
A hemispherical water tank of radius cm has cm at depth cm. During simultaneous fill and drain, .
(i) Show that .
(ii) Hence show the tank fills in seconds.
(iii) At the instant the tank is full, inflow stops and thereafter. Show that emptying takes three times as long as filling.
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?