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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 10

A spherical balloon is being inflated. At time t t\,t seconds the balloon has radius r r\,r cm and volume V V\,V cm3^33, where V=43πr3\displaystyle V = \frac{4}{3}\pi r^3V=34​πr3.

The volume of the balloon is modelled as increasing at a constant rate.

a.

Show that

drdt=kr2\displaystyle \frac{dr}{dt} = \frac{k}{r^2}dtdr​=r2k​

where k k\,k is a positive constant.

[3]
b.

The balloon is initially empty, and after 5 seconds its radius is 4 cm. Solve the differential equation to find an equation linking r r\,r and ttt.

[4]
c.

Suggest one limitation of this model.

[1]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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