A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise ?
- A. \frac{7}{3} cm ✓
- B. \frac{8}{3} cm
- C. \frac{14}{3} cm
- D. \frac{16}{3} cm
Correct Answer: A. \frac{7}{3} cm
Explanation
Volume of displaced water = Volume of the sphere. Thus, \pi (14)^2 h = \frac{4}{3}\pi (7)^3. Substituting gives 196h = \frac{4}{3} \times 343 = \frac{1372}{3}. Solving for h gives h = \frac{1372}{588} = \frac{7}{3} cm.
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