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Question
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
Solution
Radius of solid sphere = 9 m
Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 9 xx 9 xx 9`
= `3054.857` m3 .........................(i)
Diameter of cylindrical wire = 4 m
Therefore, radius = 2 m
Let length of wire be h
∴ Volume = `pir^2h`
= `22/7 xx 2 xx 2 xx h`
= `(88h)/7` m3 ................(ii)
From (i) and (ii)
⇒ `(88h)/7 = 3054.857`
⇒ `h = (3054.857 xx 7)/88`
⇒ h = 243 m
Length of the wire = 243 m
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