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The diameter of a copper sphere …

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The diameter of a copper sphere is 18 cm . It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m , find its diameter.

Posted by Muskan Singh 5 years, 2 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

Diameter of Copper Sphere = 18 cm

Radius = 9 cm [Radius = Diameter / 2]

Length of cylindrical wire = 108 m or 10800 cm [ 1 m = 100 cm]

Let radius of cylindrical wire be R

Since wire is made by melting the sphere

∴ Volume of Cylindrical wire = Volume of Copper Sphere

[Volume of Cylinder = π × Radius² × height and

Volume of Sphere = (4/3)×π×Radius³]

∴ π × R² × 10800 = (4/3) × π × (9)³

Dividing both sides by π

R² × 10800 = (4/3) × (9)³

Taking Square Root of both sides

R = 0.30 cm

Radius of wire = 0.3 cm or 3 mm

[∵ Diameter = 2×Radius]

∴Diameter of wire = 0.6 cm or 6 mm

0Thank You

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