Multiple choice

A sphere of radius $3$cm is dropped into a cylindrical vessel of radius $4$cm. If the sphere is submerged completely, then the height (in cm) to which the water rises, is

  1. $2.35$ cm.
  2. $2.30$ cm.
  3. $2.25$ cm.
  4. $2.15$ cm.
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C Correct answer
Explanation

Volume of sphere = (4/3) * pi * 3^3 = 36 * pi. This volume displaces water in the cylinder: pi * r^2 * h = 36 * pi. With r = 4, pi * 16 * h = 36 * pi, so h = 36 / 16 = 2.25 cm.

AI explanation

The volume of the submerged sphere is found using the formula 4/3 * pi * r^3, which equals 4/3 * pi * 3^3 = 36*pi cubic cm. This volume disperses within the cylindrical vessel of radius 4 cm, creating a water volume increase of pi * R^2 * h = pi * 4^2 * h. Equating the volumes yields 16*pi*h = 36*pi, so the water height h rises by 2.25 cm.

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