Multiple choice

A cylindrical vessel with internal diameter $10\ cm$ and height $10.5\ cm$ is full of water. A solid cone of base diameter $7\ cm$ and height $6\ cm$ is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take $\pi = \dfrac{22}{7}$)

  1. (i) $77\ cm^3$ and (ii) $748\ cm^3$
  2. (i) $70\ cm^3$ and (ii) $740\ cm^3$
  3. (i) $85\ cm^3$ and (ii) $786\ cm^3$
  4. (i) $88\ cm^3$ and (ii) $797\ cm^3$
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A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = (22/7) * 5^2 * 10.5 = 825 cm^3. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * (22/7) * 3.5^2 * 6 = 77 cm^3. The volume of water displaced is equal to the volume of the immersed object, which is 77 cm^3. The volume left is 825 - 77 = 748 cm^3.

AI explanation

The volume of water displaced equals the volume of the immersed cone, which is found using the formula (1/3) * pi * r^2 * h. Substituting the cone's radius of 3.5 cm and height of 6 cm gives (1/3) * (22/7) * 12.25 * 6 = 77 cm^3. The total volume of the cylindrical vessel is pi * R^2 * H, which is (22/7) * 25 * 10.5 = 825 cm^3. Subtracting the displaced water from the cylinder's total volume gives 825 - 77 = 748 cm^3 left in the vessel. This yields (i) 77 cm^3 and (ii) 748 cm^3.

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