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1.10 G: Differentiation

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Question 174

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

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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