A solid spherical ball made of iron is melted and two new balls are made whose diameters are in the ratio of 1: 2

A solid spherical ball made of iron is melted and two new balls are made whose diameters are in the ratio of 1:2. The ratio of the volume of the smaller new ball to the original ball is

  1. 1 : 3
  2. 1 : 5
  3. 2 : 9
  4. 1 : 9
  • Answer: The correct option is D
  • Explanation:

    The original ball is melted to form two new balls. The diameters of the two new balls are in the ratio 1:2. Let the diameters of the smaller and larger new balls be d and 2d, respectively.

    The volume of a sphere is = (4/3)πr3

    Radius, r = d/2

    So, V = (1/6)πd3 (Volume of proportional to the cube of diameter.)

    Volume of original ball = Volume of two new balls

    (1/6)πD3 = (1/6)πd3 + (1/6)π(2d)3

     D3 = d3 + 8d3

    D3 = 9d3

    d3/D3 = 1/9