A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is

Given: A metallic cone having base radius 2.1 cm and height 8.4 cm

Volume of a cone is given by: × π × r² × h

Let V₁ be the volume of the cone

∴ V₁ = × π × r² × h

⇒ V₁ = × π × (2.1)² × (8.4)

Volume of a sphere is given by: × π × r³

Let V₂ be the volume of the cone

∴ V₁ = × π × r³

Here,

V₁ = V₂

∴ × π × (2.1)² × (8.4) = × π × r³

⇒ r³ = × π × (2.1)² × (8.4) × = (2.1)³

⇒ r³ = (2.1)³

⇒ r = ∛(2.1)³ = 2.1 cm

∴ Radius of the sphere is 2.1 cm