2022 · Q28
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
general-mental-abilityquantitative-aptitude
- A1:3
- B1:5
- C2:9
- D1:9
Explanation
Diameters in the ratio 1:2 mean radii are also in the ratio 1:2, and volumes of spheres scale as the cube of the radius — so the two new balls have volumes in the ratio 1^3 : 2^3 = 1:8. Let the smaller ball's volume be V; the larger is 8V, and by conservation of volume the original ball's volume is 9V. The ratio of the smaller new ball's volume to the original ball's volume is therefore V : 9V = 1:9. Hence option D.