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Differentiation

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Question 140

A storage tank is modelled in the shape of a hollow cylinder. The walls of the tank are assumed to have negligible thickness. The cylinder has radius r r\,r metres and height h h\,h metres. The volume of the tank is 4 m3

a.

Show that the surface area of the tank, in m2\text{m}^2m2, is 2πr2+8r\displaystyle 2\pi r^2 + \frac{8}{r}2πr2+r8​

[4]
b.

Use calculus to find the radius of the tank for which the surface area is a minimum.

[4]
c.

Calculate the minimum surface area of the tank, giving your answer to the nearest integer.

[2]
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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