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A-LevelMathematicsDifferentiation9709/12 · May/June 2020 · Q35 Marks

A weather balloon in the shape of a sphere is being inflated by a pump. The volume of the balloon is increasing at a constant rate of 600 cm³ per second. The balloon was empty at the start of pumping.

  1. (a)Find the radius of the balloon after 30 seconds.[2]
  2. (b)Find the rate of increase of the radius after 30 seconds.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] Volume after 30 s = 18000. (4/3)πr³ = 18000
  2. [A1] r = 16.3 cm
  3. [B1] dV/dr = 4πr²
  4. [M1] dr/dt = dr/dV × dV/dt = (1 / (4πr²)) × 600
  5. [A1] dr/dt = 0.181 cm per second

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2020 Paper 1 Variant 2, question 3.

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