If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted

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

  1. 12 cm
  2. 24 cm
  3. 30 cm
  4. 36 cm

Answer

The volume of the new sphere will be equal to the combined volume of the three smaller spheres.

Let the radius of new sphere be r cm, then

4/3 πr3 = 4/3 π(63 + 83 + 103)

r3 = 63 + 83 + 103

= 1728

r = 12 cm

The correct option is A.