Question

Three solid spheres of iron whose diameters are 2 cm, 12 cm and 16 cm respectively, are melted to form a single solid sphere. Find the radius of the solid sphere.

Answer 1

Given:

Diameters = 2 cm, 12 cm, 16 cm

Hence, radii = 1 cm, 6 cm, 8 cm, respectively.

Let R be the radius of the single sphere formed. By conservation of volume, Volume of the resulting sphere = Sum of volumes of the three spheres.

`(4/3)πR^3`

= `(4/3)π(1^3 + 6^3 + 8^3)`

Cancel `(4/3)π` from both sides

`R^3` = 1 + 216 + 512 

= 729

Take cube root: R = `root3 729 = 9 cm`