Question

The diameter of a copper sphere is 6 cm . The sphere is melted and is drawn into a long wire of uniform circular cross - section . if the length of the wire is 36 cm . find its radius. ( Take π = 3.14 ) ​

Answer 1

Answer:

The wire is in the shape of a cylinder.

Since the sphere is melted and a cylindrical wire is formed, their volumes are equal.

Volume of a sphere = 4/3 πr3

As the diameter of the sphere is 6 cm, its radius

r = 3 cm

Volume of a Cylinder =πR2h

Length of the wire h = 36m = 3600cm

Hence, Volume of sphere = Volume of the wire

4/3 πr 3 = πR2h

R2 = 1/100

R= 1/10

=0.1cm

Hence, radius of the cross-section of the wire =0.1cm

Step-by-step explanation:

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Answer 2

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❒ Diamerer of the Copper sphere = 6 cm.

❒ Radius of the copper sphere, r = 6 / 2 cm = 3 cm.

❒ Volume of the sphere = 4 / 3 π r ^ 3

➡ 4 / 3 × π × ( 3 ) ^ 3 cm ^ 3

➡ 36π cm ^3

❒ Volume of the wire formed = Volume of the cylinder of length i.e. Height 36 cm

➡ π r ^ 2 h = π r ^ 2 × 36 cm^3 .

❒ Volume of copper sphere = Volume of Wire formed by recasting

➡ 36π = 36 π r ^ 2 = r ^ 2 = 1 cm ^ 2

➡ r = 1 cm.

Hence , The radius is 1 cm.

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