I was jus wondering if u noe how to do this question .The Muhibbah Company is a manufacturer of Cylindrical aluminiun tins The manager plans to rdues the cost of production The production cost is propotional to the are of the aluminium sheet used The volume that each tin can holds is 1000cm cubed { 1 litre } .1 ) Detrenima the value of h { height } , r {radius } and hence calculate the ratio of h/r aka height over radius , when the total surface area of each tin is minimum 2 ) The top and bottom pieces of the tin of height ,h cm are cut from the square-shaped aluminium sheets Determine the value of r , h , and hence calculate the ratio of h over r so that the total are of the aluminium sheet used for making the tin is minimum I really need this urgently do you know the answer ? and the method of calculation ? I need 2 methods of answering for each questions Many thanks in advance { dateline is on thursday { 9 nov 06 }
Slice a banana in half (hot-dog style cut) and spread all-natural peanut butter in between! or make a green smoothies (recipes on youtube) or trail mix: nuts, dried fruit (dried blue berries, goji berries, dried medjool dates, dried coconut chunks, or whatever you like), and cocoa nibs (bits of 100% dark chocolate - it's healthy!) All of these options are 100% healthy! :)
I eat double fiber wheat toast spread with a little peanut butter (or you could go with the wheat or fiber english muffins) and whatever serving of fruit i can get my hands onAll with about a half glass of skim milkYou could even google healthy cereals, or make some oatmeal with some fruit or egg whites and toastAll healthy!
Total surface area of a tin can A 2pr^2 + 2prh Volume of a tin can V pr^2h 1000 cm^3 Therefore, h 1000 / pr^2 Substituting this into the area equation gives : A 2pr^2 + 2pr 1000 / pr^2 2pr^2 + 2000 / r Now take the derivative of A with respect to r : dA / dr 4pr - 2000 / r^2 Set this equal to zero to find the minimum : 4pr - 2000 / r^2 0 This can be rearranged to show that : 1000 / pr^2 2r, which equals h, as shown aboveContinuing to find r, we get : r (500 / p) ^ (1/3), or approx5.42 cmNow h 2r 2 (500 / p) ^ (1/3), or approx10.84 cmThus, ratio is h / r 2r / r 2 I'm a bit confused about the second question, but I think what you want is a square sheet of aluminium, such that all 3 pieces of a can will fit, with the minimum of wastageThis would be a square sheet with the dimensions : (perimeter of can) by (height + 2 radius)Thus, Perimeter Height + 2 Radius, because the sides of a square are equalTherefore, 2pir h + 2r, so, h 2r(pi - 1) But, V pir^2h 1000, so h 1000 / (pir^2) Equating the 2 values for h gives : 2r(pi - 1) 1000 / (pir^2) from which we get : r {500 / [pi(pi - 1)]} ^ (1/3) So now we know that h 2r(pi - 1), so that after substituting for r, we get : h 2 (pi - 1) ^ (2/3) (500 / pi) ^ (1/3) And we find that the ratio h / r 2r(pi - 1) / r 2(pi - 1) Well, that was a bit of speculation, but even if I've got it wrong, then perhaps you can adapt it to your needsEdit Can't help feeling I've misunderstood the second question the first time around, but on re-reading it many times, I still don't understand it.
