June 2019 · Paper 2 · Question 13 · 10 marks☆ SaveShow the mark schemeNext questionLesson: Introduction to Differentiation and First Principles (Polynomials)
![13. r m r mh m Figure 9 [A sphere of radius r has volume 4 3ʌU࣠3 and surface area 4 ʌU࣠2] A manufacturer produces a storage tank. The tank is modelled in the shape of a hollow circular cylinde r closed at one end with a hemispherical shell at the other end as shown in Figure 9. The walls of the tank are assumed to have negligible thickness . The cylinder has radius r metres and height h metres and the hemisphere has radius r metres. The volume of the tank is 6 m3. (a) Show that, according to the model, the surface area of the tank, in m2, is given by 12 r + 5 3 ʌU࣠2 (4) The manufacturer needs to minimise the surface area of the tan k. (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 you r answer to the nearest integer. (2) 42](https://firebasestorage.googleapis.com/v0/b/plewcsat1.firebasestorage.app/o/examboard%2Fedexcel%2Fsubject%2Fmathematics%2Fa_level%2Fpure_mathematics%2Fpaper_2%2F2019%2Fjune%2Fquestions%2FQ13.png?alt=media)
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