A sphere of diameter 6\text{ cm} is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6\text{ cm}. If the sphere is completely submerged in water, then by how much will the surface level of water be raised?
- A. 0.5 cm
- B. 1 cm ✓
- C. 1.5 cm
- D. 2 cm
Correct Answer: B. 1 cm
Explanation
Radius of sphere r = 3\text{ cm}, so its volume = \frac{4}{3}\pi(3)^3 = 36\pi\text{ cm}^3. Volume of the displaced water in the cylinder = \pi R^2h = \pi(6)^2h = 36\pi h. Equating the two volumes, 36\pi h = 36\pi \implies h = 1\text{ cm}.
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