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A copper wire of diameter 6 mm is evenly wrapped on the cylinder of length 18 cm and diameter 49 cm to cover the whole surface. Find :

(i) the length

(ii) the volume of the wire.

Mensuration

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Answer

Given,

Diameter of copper wire = 6 mm = 0.6 cm

Length of cylinder (l) = 18 cm

Diameter of cylindrical base = 49 cm

Radius of cylindrical base (r) = 492\dfrac{49}{2} = 24.5 cm.

(i) Given,

Copper wire is evenly wrapped on the cylinder to cover the whole surface.

As it is covers the whole length of cylinder.

∴ No. of times it wraps around = Length of cylinderDiameter of wire=180.6\dfrac{\text{Length of cylinder}}{\text{Diameter of wire}} = \dfrac{18}{0.6} = 30.

For each turn, length of copper wire = Circumference of cylinder = 2πr

= 2 × 227\dfrac{22}{7} × 24.5

= 154 cm.

Total length = 30 × 154 = 4620 cm = 4620100\dfrac{4620}{100} = 46.20 m.

Hence, total length of copper wire = 46.20 m.

(ii) Since, wire is in the form of cylinder.

Height = Length of wire

Given,

Radius of wire (R) = 0.62\dfrac{0.6}{2} = 0.3 cm.

Volume of wire = πR2 × length

= 227×(0.3)2×4620\dfrac{22}{7} \times (0.3)^2 \times 4620

= 9147.67\dfrac{9147.6}{7} = 1306.8 cm3.

Hence, volume of wire = 1306.8 cm3.

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