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Question 1 of 4
1. Question
5 point(s)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?
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Question 2 of 4
2. Question
4 point(s)(b) Use calculus to find the value of \(r \) gives a minimum value of \(S \).
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\(r= \) \(cm \)
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Question 3 of 4
3. Question
2 point(s)(c) Prove that this value of \(r \) gives a minimum value of \(S\).
Were you able to prove this?
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Question 4 of 4
4. Question
2 point(s)(d) Find, to the nearest \(cm^2\), this minimum value of \(S \).
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\(S=\) \(cm^2\)
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