A metallic spherical shell of internal and external diameter 4 cm and 8 cm respectively, is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone is
Given: Metallic spherical shell of internal and external diameter 4 cm and 8 cm respectively
Recast into the form of a cone of base diameter 8 cm.
Volume of spherical shell is : 
× π × [(r1)3 — (r2)3] (here r1 an r2 are External and internal radii respectively)
Let v1 be the volume of given Spherical shell.
∴ v1 = 
× π × [(
)3 — (
)3] = 
× π × [(4)3 — (2)3] = 
× π × [64 — 8] = 
× π × 56 cm3
Volume of the cone is given by : 
× π × r2 × h
Let v2 be the volume of cone.
∴ V2 = 
× π × (
)2 × h = 
× π × 16 × h cm3
We know that when a object is moulded from one shape to other its volume does not change.
∴ v1=v2
That is,
× π × 56 = 
× π × 16 × h
h = 
= 
= 14
∴ h = 14cm
That is, height of the cone = 14cm