Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q3 (CAPF/2022) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

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

Result
Your answer: —  ·  Correct: D
Explanation

The volume of a sphere is directly proportional to the cube of its diameter. Let the diameters of the two new balls be 1x and 2x. Their volumes are proportional to (1x)³ = 1x³ and (2x)³ = 8x³. Since the original iron ball was melted to form these two balls, the total volume of the original ball is the sum of the volumes of the new balls: 1x³ + 8x³ = 9x³. The question asks for the ratio of the volume of the smaller new ball (1x³) to the original ball (9x³). This ratio is 1x³: 9x³, which simplifies to 1: 9. This calculation relies on the principle that volume remains conserved during melting and recasting, and that for any sphere, the volume formula V = (4/3)πr³ can be expressed in terms of diameter (d) as V = (π/6)d³.

How others answered
Each bar shows the % of students who chose that option. Green bar = correct answer, blue outline = your choice.
Community Performance
Out of everyone who attempted this question.
40%
got it right
✓ Thank you! We'll review this.

SIMILAR QUESTIONS

CAPF · 2021 · Q51 Relevance score: 3.02

Eight metallic balls of one centimetre radius each are melted into one ball. The diameter of the new ball is

NDA-II · 2012 · Q35 Relevance score: -1.19

An iron ball and a wooden ball of the same radius are released from a heigh ‘H’ in vacuum. The time taken to reach the ground will be

NDA-II · 2013 · Q19 Relevance score: -2.90

Suppose we have an iron nail and an iron ball of same mass. When submerged in water, the iron ball may float but the nail always sinks. This is because

IAS · 2002 · Q150 Relevance score: -4.06

Assertion (A) : An iron ball floats on mercury but gets immersed in water. Reason (R) : The specific gravity of iron is more than that of mercury.

NDA-II · 2016 · Q82 Relevance score: -4.09

Two balls, A and B, are thrown simul¬taneously, A vertically upward with a speed of 20 m/s from the ground and B vertically downward from a height of 40 m with the same speed and along the same line of motion. At what points do the two balls collide by taking acceleration due to gravity as 9-8 m/s*?