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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 256

A grain hopper dispenses wheat at a constant rate of 12 cm3s-1 onto a level floor, where it forms a conical pile. After t t\,t seconds, the pile has a height of h cmh\text{ cm}h cm and a volume of V cm3V\text{ cm}^3V cm3. The volume is modeled by the equation:

V=πh312 V = \frac{\pi h^3}{12} V=12πh3​
a.

Show that when t=6t = 6t=6,

dVdh=916π3 \frac{dV}{dh} = 9 \sqrt[3]{16\pi} dhdV​=9316π​
[5]
b.

Hence, find the rate at which the height of the pile is increasing when t=6t = 6t=6. Give your answer in cm s−1\text{cm s}^{-1}cm s−1 to three significant figures.

[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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