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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.
Solution
Height of the cylindrical box = h = 35 cm
Base radius of the cylindrical box = r = 10 cm
Width of metal sheet = 1 m = 100 cm
Area of metal sheet required = Total surface area of the box
`=>` Length × width = 2πr(r + h)
`=>` Length × 100 = `2 xx 22/7 xx 10(10 + 35) `
`=>` Length × 100 = `2 xx 22/7 xx 10 xx 45`
`=>` Length = `(2 xx 22 xx 10 xx 45)/(100 xx 7)` = 28.28 cm = 28 cm
∴ Area of metal sheet = Length × Width
= 28 × 100
= 2800 cm2
= 0.28 m2
∴ Cost of the sheet at the rate of Rs. 56 per m2
= Rs. (56 × 0.28)
= Rs. 15.68
Let the total sheet required be x.
Then, x – 10% of x = 2800 cm2
`=> x - 10/100 xx x = 2800`
`=> (10x - x)/10 = 2800`
`=> (9x)/10 = 2800`
`=>x = (2800 xx 10)/9`
`=>` x = 3111 cm2
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