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
34