The Muhibah Company is a manufacturer of cylindrical aluminium tinsThe manager plans to reduce the cost of productionThe production cost is proportional to the area of the aluminium sheet usedThe volume that each tin can hold is 1000 cm63 ( 1 liter).1Determne the value of h, r and hence calculate the ratio of h/r when the total surface area of each tin is minimumHere, h cm denotes the height and r cm the radius of the tin.2The top and bottom pieces of the tin of height h cm are cut from sqyare-shaped aluminium sheetsDetermine 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 minimum3Investigate the cases where the top and bottom surfaces are cut fromi) Equilateral triangleii) Regular hexagonFind the ratio of h/r for each case.Further InvestigationInvestigate cases where the top and bottom faces of the tin are being cut from aluminium sheets consisting shapes of regular
1volume h2pir^2 1000 so r^2 1000/2/pi/h surface area 2pi(h+2r^2) surface area / volume (h+2r^2)/h/r^2 1/r^2+2/h 2pih/1000+2/h which is a minimum when h is about 17.84 [(1000/pi)^0.5]
The complicating factor is that aluminium oxidizes as soon as it comes into contact with oxygen in the airEvery aluminum can thus has a sort of coating of aluminium oxideThe aluminum oxide will likely not melt the same way you'd expect aluminium metal.
A campfire does not get hot enough to melt Aluminum.
Campfires would not get that hotHowever, even if they were hot enought, the aluminum in the can would not meltIt would oxidize before it had a chance to and turn into a white powder that migles among the ashes.
Typical campfires do not get that hotThe can can become disfigured but it wont completely melt.
