A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the diameter of the sphere.

Let the Radius of cone be ‘r’ and height of cone be ‘h’

∴ r = 21 cm and h = 84 cm

Explanation: Here the volume of cone will be equal to the volume of the resulting sphere as the resulting sphere is formed by melting the cone.

Volume of cone,

⇒ V₁ = π × 441 × 28

∴ V₁ = 12348π m³→eqn1

Let the Radius of resulting sphere be ‘R’ cm

Volume of the sphere=

Now equate equation 1 and 2,

⇒ V₂ = V₁

⇒ R³ = 3087 × 3

⇒ R³ = 9261

⇒ R =∛(9261)

∴ R = 21 cm

Diameter of Sphere = 2 × radius

⇒ Diameter of Sphere = 2 × R = 42 m

Diameter of the resulting Sphere is 42 m