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 = ${\displaystyle \frac{4}{3}\pi r^3}$

 = ${\displaystyle \frac{4}{3}\times \frac{22}{7}\times 9\times 9\times 9}$

= ${\displaystyle 3054.857}$ m³ .........................(i)

Diameter of cylindrical wire = 4 m 
Therefore, radius = 2 m 
Let length of wire be h 
∴ Volume = ${\displaystyle \pi r^{2}h}$

= ${\displaystyle \frac{22}{7}\times 2\times 2\times h}$

= ${\displaystyle \frac{88h}{7}}$ m³ ................(ii)

From (i) and (ii) 

⇒ ${\displaystyle \frac{88h}{7}=3054.857}$

⇒ ${\displaystyle h=\frac{3054.857\times 7}{88}}$

⇒ h = 243 m

Length of the wire = 243 m