Education & Reference - 1 November 2006

The Muhibbah Company is a manufacturer of cylindrical aluminium tins.The manager plans to reduce the cost of production. The production cost is proportional to the area of aluminium sheet used. The volume that each tin can hold is 1000 cm³( 1 litre )
1.Determine the value of h, r and hence calculate the ratio of h/r when the total surface area of each tin is minimum. Here, h cm denotes the height and r cm the radius of the tin.
2. The top and bottom pieces of the tin of height h cm are cut from square-shaped aluminium sheets.
Determine the value for r,h and hence calculate the ratio h/r so that the total area of the aluminium sheets used for making the tin is minimum. ( refer to the diagram below )
3. Investigate cases where the top and bottom surfaces are cut from
i) Equilateral triangle
ii) Regular hexagon
Find the ratio of h/r for each case.

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what is ? show as much work as possible please!!

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i am on a limited time, i am tired, and i am confused, please help me on my math/algebra homework!!!! thanks people soooooo much!! i really aprecciate it!!

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