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Question 485

A spherical balloon is being inflated.

At time t t\,t seconds the balloon has a radius r r\,r cm and a volume V V\,V cm3.

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

a.

Show that

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

where k k\,k is a positive constant.

[3]
b.

Given that the balloon is initially empty and after 5 seconds the radius of the balloon is 4 cm.

Solve the differential equation to find an equation linking r r\,r and ttt.

[5]
c.

Suggest a limitation of the model.

[1]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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