Question

The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone. 

Answer 1

Given: Internal radius = 3 cm

External radius = 5 cm

Volume of spherical shell   

= `4/3pi(r^3 - r^3)` 

= `4/3pi(5^3 - 3^3)` 

= `4/3 xx 22/7(125 - 27)` 

= `4/3 xx 22/7 xx 98` 

Volume of solid circular cone 

= `1/3pir^2h` 

= `1/3 xx 22/7 xx r^2 xx 32` 

Vol. of cone = Vol. of sphere 

`=> 1/3 xx 22/7 xx r^2 xx 32`

`=> 4/3 xx 22/7 xx 98` 

`=> r^2 = (4 xx 98)/32` 

∴  `r = 2 xx 7/2`

∴  r = 7 cm