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