Question

Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m. 

Answer 1

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