Multiple choice

A sphere of radius $6 cm$ is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is $8 cm$. If the sphere is Submerged completely, then the surface of the water rises by

  1. $4.5 cm$
  2. $4 cm$
  3. $3 cm$
  4. $2 cm$
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * 6^3 = 288pi. Volume of water rise = pi * 8^2 * h = 64pi * h. 64pi * h = 288pi. h = 288/64 = 4.5 cm.

AI explanation

The volume of the submerged sphere equals the volume of the displaced water, which is calculated using the formula for the volume of a sphere, V = (4/3) * pi * r^3. Substituting the radius of 6 cm gives a volume of (4/3) * pi * 6^3, which equals 288 * pi cubic centimeters. This volume is spread across the circular base of the cylindrical vessel with radius 8 cm, forming a cylindrical column of water whose height is found using V = pi * R^2 * h. Setting 288 * pi = pi * 8^2 * h yields 288 = 64h, so the rise in water level h is 4.5 cm.

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