Question

A hollow sphere of internal and external radii 2cm and 4cm is melted into a cone of basse radius 4cm. find the height and slant height of the cone______?

Answer 1

Given that internal radii of hollow sphere (r) = 2cm

External radii of hollow sphere (R) = 4cm

Volume of hollow sphere = `4/3pi(R^2-r^2)`

`v_1=4/3xxpi(4^2-2^2)`         ..........(1)

Given that sphere is melted into a cone

Base radius of cone = 4cm

Let slant height of cone be l

Let height of cone be h

`l^2=r^2+h^2`

`l^2=16+h^2`               ..............(3)

Volume of cone`=1/3pir^2h`

`v_2=1/3pi(4)^2h`         .................(2)

v_{1 =} v₂ Equating (1) and (2)

`4/3pi(4^2-2^2)=1/3pi(4)^2h`

`(4/3pi(16-4))/(1/3pi(16))=h`

h = 14cm

Substituting ‘h’ value in (2)

`l^2=16+h^2`

`l^2=16+14^2`

l² = 16 + 196

l = 14.56cm

∴ Slant height of cone = 14.56cm