Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. 

Answer 1

External diameter= 8 cm 
Therefore, Radius (R) = 4 cm 
Internal diameter = 4 cm 
Therefore, Radius (r) = 2 cm 
Volume of metal used = `4/3pi(R^3 - r^3)`

= `4/3 xx 22/7 xx (4^3 - 2^3)`

= `4/3 xx 22/7 xx 56`

= 234.66 cm³ ................(i)

Diameter of the oone = 8 cm 
Therefore, radius = 4 cm 
Let height of the cone = h 
Volume = `1/3pir^2h = 1/3 xx 22/7 xx 4 xx 4 xx h = (352h)/21` .......(ii)

From (i) and (ii) 

⇒ `(352h)/21 = 234.66`

⇒ 352h = 4927.86

⇒ h = 13.99 cm = 14 cm

The height of the cone = 14 cm