Question

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is

Options

• 12 cm

•  24 cm

•  30 cm

• 36 cm

Answer 1

Let r be the radius of single sphere.

Now,

The volume of single sphere = sum of volume of three spheres

`4/3pir^3 = 4/3pi(61)^3 + 4/3 pi(8)^3 + 4/3 pi(10)^3`

`4/3pir^3 = 4/3 pi(216 + 512 + 1000)`

       `r^3 = 1728`

         `r = 12 cm`

Hence, the diameter = 20 × r = 24 cm