14 An open-topped fish tank is to be made for an aquarium.
It will have a square horizontal base, rectangular vertical sides and a volume of \(60 \mathrm {~m} ^ { 3 }\)
The materials cost:
- \(\pounds 15\) per \(\mathrm { m } ^ { 2 }\) for the base
- \(\pounds 8\) per \(\mathrm { m } ^ { 2 }\) for the sides.
14
- Modelling the sides and base of the fish tank as laminae, use calculus to find the height of the tank for which the overall cost of the materials has its minimum value.
Fully justify your answer.
[0pt]
[8 marks]
14 - In reality, the thickness of the base and sides of the tank is 2.5 cm
Briefly explain how you would refine your modelling to take account of the thickness of the sides and base of the tank of the tank.
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[1 mark]
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14
- (ii) How would your refinement affect your answer to part (a)?
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[1 mark]