Question

Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

Answer 1

Let R be the radius of single solid sphere.

Therefore,

Volume of single solid sphere = volume of all three spheres

`4/3 piR^3 = 4/3 pir_1^3 + 4/3 pir_2^3 + 4/3 pir_3^3`

`4/3 piR^3 = 4/3 pi (r_1^3 +r_2^3 + r_3^3)`

      `R^3 = (3^3 + 4^3 + 5^3)`

      `R^3 = 27 + 64 + 125`

`R^3 = 216`

   `r = sqrt(216)`

     ` = 6`

  `R = 6`

Hence, the radius of single solid sphere = 6 cm.