Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that the width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of rupees 56 per m. Find the area of metal sheet required, if 10 percent of it is wasted in cutting, overlapping, etc.
Answers
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
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