Question

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A copper wire , 33 mm in diameter ,is would about a cylinder whose length is 12 cm ,and diameter 10 cm , so as to cover the curved surface of the cylinder. Find the length and mass of the wire , assuming the density of copper to be 8.88 g per cm^3.

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Class - 10th

Chapter Name - Surface area of volumes.

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Answer 1

SOLUTION

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It is assumed that one round of copper wire will cover 3mm or 0.3cm height of cylinder.

Number of rounds = Height of the cylinder ÷ Diameter of the wire

= 12/0.3

=40rounds

Now, the length of the wire required in one round = Circumference of the base of the cylinder.

Diameter of the cylinder =10cm,

so the radius =5cm.

Therefore circumference =2πr = 2π×5 =10π

Length of wire required in one round =10π

Length of wire required in 40 rounds =10π×40

=400×3.14

∴ Length of the wire =1257.14cm

Radius of the wire = 0.3/2

=0.15cm

Volume of wire = Area of cross section of wire × length of the wire

=πr2×1257.14

=3.14×(0.15)square×1257.14

∴ Volume of the wire =88.898cm3

Mass = Density × Volume

=8.88×88.898

∴ Mass =789.41gm

Answer 2

Answer:

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