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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? - Mathematics

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 = πr2h

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

=1mm = 0.1cm

`V_2=pi(0.1)^2h`       ..........(2)

Equating (1) and (2)

V1 = V2

⇒ 381.703 = π(0.1)2h

⇒ h = 12150cm

∴ Length of wire (h) = 12150cm

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 14 | Page 28
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