Question

The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre. 

Answer 1

Radius of sphere = 9 cm 

Volume of sphere = `4/3pir^3`

= `4/3 xx 22/7 xx 9 xx 9 xx 9`

= `3054.857  "cm"^3 = 30.55 xx 10^-4   "m"^3`   .....(i)

Diameter of cylindrical wire = 2 mm 
Therefore, radius = 1 mm = 0.001 m 
Let length of wire be h 
∴ Volume = `pir^2h`

= `22/7 xx 0.001 xx 0.001 xx h`

= `3.142h xx 10^-6` m³ ....................(ii)

From (i) and (ii) 

⇒ `3.142 xx 10^-6h = 30.55 xx 10^-4`

⇒ `h = (30.55 xx 10^-4)/(3.142 xx 10^-6)`

⇒ h = 972m

Length of the wire = 972 m