A cylinder is half-filled with liquid. If radius doubles and height halves, what's the new filled depth percentage-wise?
Show answer & explanation
Correct answer: A
Explanation
Cylinder half-filled ⇒ Filled height = h/2
Volume = πr²h
Initial liquid volume = (1/2)πr²h
New cylinder: r → 2r, h → h/2
New volume = π(2r)²(h/2) = 2πr²h
New filled height = (Liquid volume / New base area)
= [(1/2)πr²h] / [π(2r)²]
= [(1/2)πr²h] / [4πr²]
= h/8
New total height = h/2
Percentage = (h/8) / (h/2) × 100 = 25%