Multiple choice

A large solid metallic cylinder whose radius and height are equal to each other is to be melted and 48 identical solid balls are to be recast from the liquid metal so formed. What is the ratio of the radius of a ball to the radius of the cylinder ?

  1. 1:4

  2. 2:3

  3. 4:1

  4. 3:2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let cylinder radius = R, height = R (since they're equal). Cylinder volume = πR² × R = πR³. Volume of 48 balls = 48 × (4/3)πr³ = 64πr³. Equating volumes: πR³ = 64πr³, so R³ = 64r³, giving R = 4r. Therefore r/R = 1/4, or ratio is 1:4. Option A is correct.

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