Multiple choice

A cylindrical rod of iron whose radius is one fourth of its height is melted and cast into spherical balls of the same radius as that of the cylinder. What is the number of spherical balls ?

  1. 3

  2. 4

  3. 2

  4. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let cylinder height = h, so radius = h/4. Cylinder volume = π(h/4)²h = πh³/16. Sphere volume = (4/3)π(h/4)³ = πh³/48. Number of spheres = Cylinder volume / Sphere volume = (πh³/16)/(πh³/48) = 48/16 = 3. The h³ terms cancel out neatly, showing the answer is independent of the actual height.

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