Question

A hollow sphere of internal and external diameter 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 in hollow sphere = `4/3pi(R^3 - r^3)`

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

= `88/21(64 - 8)`

= `88/21 xx 56  cm^3`  ...(i) 

Diameter of cone = 8 cm

Therefore, radius = 4 cm

Let height of cone = h 

∴ Volume = `1/3pir^2h`

= `1/3 xx 22/7 xx 4 xx 4 xx h`

= `352/21 h`  ...(ii)  

From (i) and (ii) 

`352/21 h = 88/21 xx 56` 

`=> h = (88 xx 56 xx 21)/(21 xx 352) = 14  cm` 

Height of the cone = 14 cm.