A sphere of radius 5 cm is dropped in a right circular cylindrical vessel partly filled with water. The radius of the cylindrical vessel is 10 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?
- A. \frac{5}{3} cm ✓
- B. \frac{5}{2} cm
- C. 1 cm
- D. \frac{5}{6} cm
Correct Answer: A. \frac{5}{3} cm
Explanation
The volume of water displaced equals the volume of the submerged sphere. So, \pi R^2 h = \frac{4}{3}\pi r^3. Substituting R = 10 and r = 5, we get \pi(10^2)h = \frac{4}{3}\pi(5^3) \implies 100h = \frac{500}{3}. Solving for h yields h = \frac{5}{3} cm.
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