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Question
The radius of a metal sphere is 3 cm. The sphere is melted and made into a long wire of uniform circular cross-section, whose length is 36 cm. To calculate the radius of wire, complete the following activity.
Radius of the sphere = `square`
Length of the wire = `square`
Let the radius of the wire by r cm.
Now, Volume of the wire = Volume of the `square`
`square` = `square`
r2 × `square` = `square` × `square`
r2 × `square` = `square`
r = `square`
Hence, the radius of the wire is `square` cm.
Solution
Radius of the sphere = 3 cm
Length of the wire = 36 cm
Let the radius of the wire by r cm.
Now, Volume of the wire = Volume of the sphere
πr2h = `bb(4/3)` πR3
r2 × 36 = `bb(4/3)` × 33
r2 × 36 = 36
r = 1
Hence, the radius of the wire is 1 cm.
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