Multiple choice

A sphere of diameter 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is completely submerged in water, then by how much will the surface level of water be raised?

  1. 0.5 cm

  2. 1 cm

  3. 1.5 cm

  4. 2 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 3^3 = 36 * pi. Volume of displaced water in cylinder = pi * R^2 * h = pi * 6^2 * h = 36 * pi * h. Equating volumes: 36 * pi = 36 * pi * h => h = 1 cm.

AI explanation

Because the sphere is completely submerged, the volume of the displaced water equals the volume of the sphere, so pi times the vessel radius squared times the height increase equals four-thirds times pi times the sphere radius cubed. Substituting the vessel radius of 6 cm and the sphere radius of 3 cm gives pi * 6^2 * h = (4/3) * pi * 3^3. Solving for h gives 1 cm.

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