Question

find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylinderical box of diameter 20cm and height 35cm.given that the width of the metal sheet is 1 m.also find the cost of the sheet at the rate of ruppees 56 per meter

Answer 1

let length of metal sheet be l and breadth be b
Breadth     b = 1m = 100 Cm

radius of cylindrical box r = 10 Cm
and      Height               h = 35 Cm

Thus area of of closed cylindrical box = 2pi r h + 2 pi r^2
                                                             = 2*3.14*10*35 + 2*3.14*100
                                                             = 2198 + 628
                                                            = 2826 Cm sq
      Thus

Area of box = area of Sheet

                                    2826 = l * b
                                       l = 2826/100
                                       l = 28.26 Cm
Thus length of sheet is 28.26 Cm

Cost of 1 msq of sheet = 56 Rs
Cost of 10000Cm Sq = 56/10000 Rs
Cost of 2826 Cmsq = 56 * 0.2826 Rs
                                = 15.8256 Rs
Thus total cost of sheet is 15.8256 Rs