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Question
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Solution
Given that,
Diameter of sphere = 6cm
Radius of sphere =`d/2=6/2cm=3cm=r_1`
Diameter of the wire = 0.2cm
Radius of the wire =0.1cm = `r_2`
Volume of sphere = Volume of wire
⇒`4/3πr_1^3=πr_2^2h`
⇒`4/3xx3xx3xx3=0.1xx0.1xxh`
⇒`(4xx3xx3)/(0.1xx0.1)=h`
⇒h=3600
⇒ h =36m.
∴ Length of wire=36m.
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