Question

Three metallic spherical balls of radii5 cm, 4 cm and 3 cm are melted together and recast into a big spherical ball. Find the radius of the big ball.

Answer 1

Given:

Three solid metallic spheres with radii 5 cm, 4 cm and 3 cm.

They are melted and recast into one large sphere.

Volume of a sphere = `(4/3)π r^3`

Total volume of the three small spheres

= `(4/3)π(5^3) + (4/3)π(4^3) + (4/3)π(3^3)`

= `(4/3)π(125 + 64 + 27)`

= `(4/3)π(216)` cm³

Let R be the radius of the large sphere. By conservation of volume,

= `(4/3)π R^3`

= `(4/3)π(216)`

Cancel `(4/3)π` from both sides:

R³ = 216

Therefore, R = `root 3 216`

= 6 cm