Multiple choice

A cylinder vessel of base radius 14 cm is filled with water to some height If a rectangular solid of dimensions 22 cm X 7 cm X 5 cm is immersed in it what is the rise in water level?

  1. 0.5 cm

  2. 1.0 cm

  3. 1.25 cm

  4. 1.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of solid = 22 * 7 * 5 = 770 cm^3. Volume of cylinder rise = pi * r^2 * h. 770 = (22/7) * 14 * 14 * h. 770 = 22 * 2 * 14 * h = 616 * h. h = 770 / 616 = 1.25 cm.

AI explanation

Using the principle of water displacement, the volume of the immersed rectangular solid equals the volume of the displaced water. The volume of the solid is 22 cm times 7 cm times 5 cm, which equals 770 cubic cm. The volume of displaced water is calculated as the base area of the cylindrical vessel times the rise in water level, giving pi times 14 squared times the rise. Setting them equal gives 770 equals 22 times 7 times the rise, so the rise in water level is 1.25 cm.

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