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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 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 Rs. 56 per m. Find the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.

A
18cm and Rs. 15.68 ; 3,111 cm2
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B
28cm and Rs. 15.68 ; 3,111 cm2
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C
38cm and Rs. 15.68 ; 3,111 cm2
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D
48cm and Rs. 15.68 ; 3,111 cm2
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Solution

The correct option is B 28cm and Rs. 15.68 ; 3,111 cm2
Given, a hollow and close cylinder of diameter 20 cm and height 35 cm. width of sheet is 1m and cost of sheet is Rs. 56/m.
Radius = d2 =10 cm
So,we have to find total surface area.
Total surface area =2πr(r+h)
=2×227×10×(10+35)
=2828.57 cm2
=0.282m2
Cost of sheet =0.282×56
= Rs.15.8
Length of sheet =Areaofsheetwidthofsheet=0.2821=0.28 m =28 cm
Area of metal sheet if 10% is wasted then sheet required = Area of sheet + 10% of sheet
=2828.57+10% of 2828.57
=2828.37+282.8
=3111.57cm2

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