Practice variation 1 of 3
Rates of change — Same tank with constant $\alpha$
Your question
A hemispherical tank of radius has volume when the water depth is . While filling and draining, for a positive constant .
(i) Show that .
(ii) Hence show that the tank is full after seconds.
(iii) When full, inflow stops and draining continues with . Show that the tank takes seconds to empty.
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?