please help answer these questions The Muhibbah 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 1000cm? (1 liter)1Determine 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 tin2The top and bottom pieces of the tin of height h cm are cut from squre-shaped aluminium sheetsDetermine the value for r, h hence calculate the ratio h/r so that the total area of the aluminium sheets used for making the tin is minimum3Investigate cases where the top and bottom surfaces are cut from iEquilateral triangle iiRegular hexagon Find the ratio of h/r for each case
First, remember the formula for surface area of a cylinder, which is pretty easy; the top and bottom are circles, and the rest is basically a rectangle (with the width equal to the circles' circumference) curled upAlso the formula for volume, which is piR^2H1000, so you can use some substitution to eliminate either R or H in your SA formulaSo now you've got SA as a function of R or H, depending on which you removed.To find the minimum, remember that a maximum or minimum is where the derivative (dA/dR or /dH) is zeroThat should get you 1.
