Question

A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

Answer 1

Given that
Hollow sphere external radii = 4cm = `r_2`
Internal radii `(r_1)`=2cm
Cone base radius (R) = 4cm
Height = ?
Volume of cone = Volume of sphere
⇒ `1/3πr^2H=4/3π(R_2^3-R_1^3)`

⇒ `4^2H=4(4^3-2^3)`

⇒`  H=H=(4xx56)/16=14cm`

Slant height =`sqrt(R^2+H^2)=sqrt(4^2+14^2)`

⇒ `l= sqrt(16+196)=sqrt(212)`

=14.56cm.