Find the minimum length in cm and correct to the nearest whole number of a thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. The width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m. Find the area of the metal sheet required if 10% of it is wasted in cutting, overlapping etc.
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Let length of metal sheet be l and breadth be b
Breadth = b = 1m = 100 Cm
Radius of cylindrical box r = 10 Cm
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.
So, 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 2826Cm sq. = 56 * 0.2826 Rs
= 15.8256 Rs
Thus total cost of sheet is 15.8256 Rs.
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