The diameter of a metallic sphere is equal to 9cm. it is melted and drawn into a long wire of diameter 2mm having uniform cross-section. Find the length of the wire?

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#### Solution

Given diameter of a sphere (d) = 9cm

Radius(r) = `9/2` = 4.5cm

Volume of a sphere = `4/3pir^3`

`V_1=4/3xxpixx4.5^3=381.70cm^3` ...........(1)

Since metallic sphere is melted and made into a cylindrical wire

Volume of a cylinder = πr^{2}h

Given radius of cylindrical wire(r) =`2mm/2`

=1mm = 0.1cm

`V_2=pi(0.1)^2h` ..........(2)

Equating (1) and (2)

V_{1} = V_{2}

⇒ 381.703 = π(0.1)^{2}h

⇒ h = 12150cm

∴ Length of wire (h) = 12150cm

Concept: Volume of a Combination of Solids

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