2009 June C2 Q9
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Earned Point(s): 0 of 0, (0) The diagram above shows a closed box used by a shop for packing pieces of cake. The box is a right prism of height h cm. The cross section is a sector of a circle. The sector has radius \(r cm\) and the angle \(1\) radian. The volume of the box is \(300cm^3\). (a) Show that the surface area of the box, \(S cm^2\), is given by \(S =r^2+\frac{1800}{r}\). Were you able to show this? (b) Use calculus to find the value of \(r \) gives a minimum value of \(S \). \(r= \) \(cm \) (c) Prove that this value of \(r \) gives a minimum value of \(S\). Were you able to prove this? (d) Find, to the nearest \(cm^2\), this minimum value of \(S \). \(S=\) \(cm^2\)
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