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
work is defined as distance x forcePower is work per unit of timeForce is measured in Newtons1 Newton 1 kg m/sec^2Unless I'm mistaken, the time it takes can be calculated by work/power.
I will answer the first question and maybe you can figure out the second two for yourselfgiving you the dimensions of r and h you can find the ratio and the rest of the informationWhen you approach the other problems try to find the area of the shape you are trying to solve for and substitute for any second variable by soving for h in the volume then plugging into the total area before you take the derivativeArea of the square tops: 2 2r^2 Area of the side: 2 pi(r^2) Total Area after multiplying out: 8r^2 + 2pi(rh) Then find a substitute for for h because you can't take the derivative of two variablesyou can get the substitute from the volume Volume 1000pi (r^2h) h 1000/2pi (r^2) Area 8r^2 + 2pi (r) (1000/2pir^2) Area 8r^2+2000/r Area' 16r-(2000/r^2) 16r^32000 .r3.969 h20.206 GOOD LUCK!!!
The potential energy of the pinao at its full height is Ep mgh mmass, ggravity, hheight Ep 109.8300 29,400 joules Power 400 watts1 watt 1 joule/second 400 J/s If Ep is in joules and P is in joules/second then to work out the number of seconds divide Ep/P - the units cancel out leaving only secondstime Ep/P 29,400/400 73.5 seconds
Total energy requirement power x time mgh P x t 3x10^2x9.8x10 4.00x10^2 x t; all quantities in MKS so t is in seconds, t (3x98)/4 73.5 s 1 m 13.5 s It will take some what more time in actual practice as we have not accounted for any losses due to frictional forces and also piano is not brought up all the time remaining at restSo there is some average kinetic energy of the piano as well as the crane parts.
