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Differentiation

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Question 115

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

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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