A hollow metallic Sphere with external diameter8cm and internal diameter 4cm is melted and moulded into a cone having base diameter 8cm. The height of the cone is
Given: A hollow metallic Sphere with external diameter8cm and internal diameter 4cm
A cone having base diameter 8cm
Radius of the cone is: 
= 4cm
External Radius of the sphere is 
= 4cm
Internal Radius of the sphere is 
= 2cm
Volume of a Hollow Sphere is given by: 
π((r1)3 – (r2)3) (here r1 and r2 are External and internal radii of the hollow sphere respectively)
Let V1 be the Volume of the Hollow sphere.
∴ V1 = 
π((r1)3 – (r2)3)
⇒ V1 = 
π((4)3 – (2)3) = 
π(64 – 8) = 
π(56)
Volume of the cone is given by 
× π × r2 × h
Let V2 be the volume of the cone
∴ V2 = 
× π × r2 × h
⇒ V2 = 
× π × (4)2 × h
Here, Hollow sphere is melted and moulded into a cone.
∴ V1 = V2
⇒ 
π(56) = 
× π × (8)2 × h
⇒ 
× π × 16 × h = 
× π × (56)
⇒ h = 
= 14cm
∴ Height of the cone is 14cm