The height and radius of base of a metallic cone are 27 cm and 16 cm respectively .It is melted and recast into a sphere .Find the radius and curved surface of the sphere.

Answer

`3:1:2`

Explanation

Height of cone h =27 cm
Radius of cone r=16 cm
Volume of cone `=(1)/(3)pir^(2)h=(1)/(3)pi(16)^(2)xx27cm^(3)`
Let radius of sphere=R
Volume of sphere =`(4)/(3)piR^(3)`
Volume of sphere =volume of cone
`(4)/(3)piR^(3)=(1)/(3)pi(16^(2))xx27`
`R^(3)=(16^(2)xx27))/(4)=4^(3)xx3^(3)`
R=4`xx` 3=12cm
Curved surface of sphere =`4piR^(2)=4pi(12^(2))=576 pi cm t^(2)`