How much water will remain in the vessel after the overflow?
Consider the following for the next three (03) items that follow:<br><br>A conical vessel of radius 12 cm and height 16 cm is filled with water. A sphere is lowered into water and its size is such that it touches the sides of the vessel and it is just immersed.
- A. 288\pi\text{ mL}
- B. 360\pi\text{ mL}
- C. 480\pi\text{ mL} ✓
- D. 500\pi\text{ mL}
Correct Answer: C. 480\pi\text{ mL}
Explanation
Volume of the conical vessel is \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi(12)^2(16) = 768\pi. Volume of the sphere is \frac{4}{3}\pi R^3 = \frac{4}{3}\pi(6)^3 = 288\pi. The remaining water is the difference: 768\pi - 288\pi = 480\pi\text{ mL}.
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