A conical vessel whose internal radius is 5\text{ cm} and height 24\text{ cm} is full of water. The water is emptied into a cylindrical vessel with internal radius 10\text{ cm}. What is the height to which the water rises?
- A. 1 cm
- B. 2 cm ✓
- C. 3 cm
- D. 4 cm
Correct Answer: B. 2 cm
Explanation
Volume of water in the cone = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi(5)^2(24) = 200\pi\text{ cm}^3. When poured into the cylinder, \pi(10)^2 H = 200\pi \implies 100\pi H = 200\pi \implies H = 2\text{ cm}.
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