Edexcel Mathematics Sample paper · Paper 2 · Question 14 · ExamRizz

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Sample paper · Paper 2 · Question 14 · 9 marks

14. A company decides to manufacture a soft drinks can with a capacity of 500 ml. The company models the can in the shape of a right circular cylinder with radius r cm and height h cm. In the model they assume that the can is made from a metal of negligible thickness. (a) Prove that the total surface area, S cm2 , of the can is given by 1000 S = 2 π r2 + r (3) Given that r can vary, (b) find the dimensions of a can that has minimum surface area. (5) (c) With reference to the shape of the can, suggest a reason why the company may choose not to manufacture a can with minimum surface area. (1)

Lesson: Introduction to Differentiation and First Principles (Polynomials)