Multiple choice

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

  1. $\dfrac{2}{9}cm$
  2. $\dfrac{4}{9}cm$
  3. $\dfrac{9}{4}cm$
  4. $\dfrac{9}{2}cm$
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C Correct answer
Explanation

Volume of sphere = (4/3)*pi*3^3 = 36*pi. Volume of water displaced in cylinder = pi*r^2*h = pi*4^2*h = 16*pi*h. Setting 16*pi*h = 36*pi, h = 36/16 = 9/4.

AI explanation

The volume of the immersed sphere, (4/3) * pi * 3^3, equals the volume of the displaced water in the cylindrical vessel, pi * 4^2 * h. Setting the volumes equal gives pi * 36 = pi * 16 * h. Solving for the rise in water level h yields 9/4 cm.

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