Question

how much sq metre of sheet is required to make 50 cylinders of 20 cm height and diameter of 14 cm? If cost of 1 sq m cost of sheet is rs. 200 then how much will be expenditure?

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Answer 1

Hope you like my process
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=> Let the area of sheet required to make a cylinder be x cm²

=> For 50 cylinders , required area =50x cm²

=> Now the area to make a cylinder by a sheet will be equal to curve surface area of cylinder.

=> curve surface area = 2πrh

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Given
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=> Height (h) = 20 cm

=> diameter (d) = 14 cm

=> Radius (r) = d/2 = 7 cm

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now

=> x = 2πrh= 2×(22/7)×7×(20)

=> x = 44×20= 880 cm²
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Note
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=> 100 cm = 1 m

=> 10000 cm² = 1 m²

=> 880 cm² = 0.088 m²
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So required area of sheet = 50x

= 50× 0.088 = 4.4 m²____(answer)

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If 1 m² costs Rs 200 then

=> 4.4 m² sheet costs 200×4.4 =Rs 880 __(answer)

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Answer 2

Considering cylinder without top and bottom
The required sheet to make 50 cylinders =CSA of the cylinder×50
=2πrh×50
=2×(22/7)×7×20×50
=2×(22/7)×7×20×50
=22×20×100
=44000 sq cm
=44000/(100×100) sq m
=4.4 sq m
cost of 1 sq m sheet=₹ 200
cost of 4.4 sq m sheet=200×4.4
=₹880



2nd Case

considering that the cylinder is closed.

The required sheet to make 50 cylinders =TSA of the cylinder×50
=2πr(r+h)×50
=2×(22/7)×7(7+20)×50
=2×(22/7)×7×27×50
=22×27×100
= 59400 sq cm
=59400/10000. sq m
=5.94 sq m
cost of 1 sq m sheet=₹ 200
cost of 5.94 sq m sheet=200×5.94
=₹1188