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Differentiation

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Question 443

A spherical snowball is melting in the sun. The volume, VVV, of the snowball is decreasing at a constant rate.

Show that the rate of decrease of the snowball's surface area, AAA, is inversely proportional to its radius, rrr.

You may use the following formulae for a sphere:

V=43πr3andA=4πr2 V = \frac{4}{3}\pi r^3 \quad \text{and} \quad A = 4\pi r^2 V=34​πr3andA=4πr2
[5]
Markscheme

Differentiation Questions

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

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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