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2015 · Q50

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

Elementary MathematicsMensuration
  1. A1.5 cm
  2. B2 cm
  3. C2.25 cm
  4. D4.5 cm

Explanation

This is an Archimedes displacement problem. The sphere's volume is (4/3)π(3³) = 36π cm³, and this volume of water is displaced into the vessel's cross-section π(4²) = 16π cm². The rise in level is 36π/16π = 2.25 cm. Option (d) 4.5 cm is the trap from using the sphere's diameter instead of its radius. Hence option (c).