A tank containing water is in the form of a hemisphere. The axis is vertical, the lowest point is A and the radius is r, as shown in the diagram. The depth of water at time t is h. At time t = 0 the tank is full and the depth of the water is r. At this instant a tap at A is opened and water begins to flow out at a rate proportional to √h. The tank becomes empty at time t = 14. The volume of water in the tank is V when the depth is h. It is given that V = ⅓π(3rh² – h³).

Q: What topic does this question test?

This question tests Differential equations in A-Level Mathematics (syllabus code 9709). It is worth 12 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics May/June 2020 examination, Paper 3 Variant 3 (9709_s20_qp_33.pdf).

Question

A tank containing water is in the form of a hemisphere. The axis is vertical, the lowest point is A and the radius is r, as shown in the diagram. The depth of water at time t is h. At time t = 0 the tank is full and the depth of the water is r. At this instant a tap at A is opened and water begins to flow out at a rate proportional to √h. The tank becomes empty at time t = 14. The volume of water in the tank is V when the depth is h. It is given that V = ⅓π(3rh² – h³).

Oracle Prep · Accepted Answer

Sign up to Oracle Prep to view the full model answer with examiner insights.

📋 Examiner Report & Trap Analysis

🎯 Mark Scheme Breakdown

Unlock the Examiner's Analysis

About This A-Level Mathematics Question

Topic

Source

Practice on Oracle Prep

Related Mathematics Questions