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Question
A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width.
Solution
We have,
Radius of the metallic sphere, R`= 8/2 = 4 "cm"` and
Height of the cylindrical wire, h = 12 m = 1200 cm
Let The radius cylindrical wire, h = 12 m = 1200 cm
Let the radius of the base be r.
Now,
Volume of the cylindrical wire = Volume of the metallic sphere
`=> pi"r"^2"h" = 4/3 pi"R"^3`
`=> "r"^2 = (4"R"^3)/(3"h")`
`=> "r"^2 = (4xx4xx4xx4)/(3xx1200)`
`=> "r"^2 = 16/225`
`=> "r" =sqrt(16/25)`
`=> "r" = 4/15 "cm"`
∴ The width of the wire = 2r
`=2xx4/15`
`=8/15 "cm"`
So, the width of the wire is `8/15` cm.
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