Multiple choice

A cylindrical vessel, whose radius is 6 cm, contains water. If a solid sphere of radius 3 cm is dipped into the vessel completely, then what is the rise in the water level in the vessel?

  1. 3 cm

  2. 2 cm

  3. 1 cm

  4. 0.5 cm
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C Correct answer
Explanation

The volume of the sphere submerged equals the volume of the water displaced. Volume of sphere = (4/3) * pi * 3^3 = 36 * pi. Volume of water rise in cylinder = pi * r^2 * h = pi * 6^2 * h = 36 * pi * h. Equating the two: 36 * pi = 36 * pi * h, so h = 1 cm.

AI explanation

The rise in water level is calculated by dividing the volume of the submerged sphere by the base area of the cylindrical vessel. The volume of the sphere is four-thirds times pi times 3 cubed, which equals 36 pi cubic cm. The base area of the vessel is pi times 6 squared, which equals 36 pi square cm. Dividing 36 pi by 36 pi gives a rise of 1 cm.

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