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Question
The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.
Solution
Diameter of sphere = 42 cm
Radius of sphere = 21 cm
Volume of sphere `= 4/3pir^3 = 4/3pixx21xx21xx21 "cm"^3`
Diameter of wire = 2.8 cm
Radius of wire =1.4 cm
Let the length of the wire be / cm.
The volume of the sphere is equal to the volume of the wire therefore,
`pixx1.4xx1.4xxl = 4/3pixx21xx21xx21`
`l =(4xx21xx21xx21)/(3xx1.4xx1.4) = 6300 "cm" = 63 "m"`
So, the wire is 63 m long.
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