Multiple choice

The radius of a cylindrical vessel is $7cm$ and its height is $12cm$. $\cfrac{2}{3}$ of the vessel is filled with water. A sphere having radius $6cm$ is dropped into the water. Find the volume of the water that will come out of the vessel.

  1. $196\pi$ ${cm}^{3}$
  2. $92\pi$ ${cm}^{3}$
  3. $288\pi$ ${cm}^{3}$
  4. $588\pi$ ${cm}^{3}$
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B Correct answer
AI explanation

When the sphere is dropped into the water, the volume of water that overflows equals the volume of the sphere, provided the sphere is fully submerged. Using the sphere volume formula (4/3) * pi * r^3 with radius 6 cm, we get (4/3) * pi * 6^3 = 288pi. The available water in the vessel is only (2/3) * pi * 7^2 * 12 = 392pi, which is greater than the sphere's volume, meaning the sphere is completely submerged and exactly 288pi cubic cm of water will overflow.

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