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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 109

The volume of a sphere is increasing at a constant rate of 2 cm3 ^3\,3s−1^{-1}−1.

The volume of a sphere of radius r r\,r cm is 43πr3\displaystyle \frac{4}{3}\pi r^334​πr3 cm3^33, and its surface area is 4πr2 4\pi r^2\,4πr2 cm2^22.

a.

Show that the rate of increase of the radius when r=2r = 2r=2 is aπ\displaystyle \frac{a}{\pi}πa​ cm s−1^{-1}−1, where a a\,a is a constant to be found.

[4]
b.

Find the rate at which the surface area is increasing when r=2r = 2r=2.

[3]
Markscheme

3.6 Differentiation (A-level only) Questions

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

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

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