Single correct option
A cylindrical tank of radius 7 m and height 10 m is completely full of water. All this water is emptied into an empty conical vessel that has the same base radius (7 m) and a height of 45 m. What fraction of the conical vessel's volume gets filled with water?
- A. 1/3
- B. 4/9
- C. 2/3
- D. 3/4
Show answer and solution
Answer: (C) 2/3
Volume of water = volume of cylinder = πr²h = π(7)²(10) = 490π cubic m. Full volume of the cone = (1/3)πr²H = (1/3)π(7)²(45) = 735π cubic m. Fraction filled = 490π/735π = 490/735 = 2/3. Notice the radius cancels out, so only the ratio of heights (scaled by the 1/3 factor for the cone) matters: fraction = 10/(45/3) = 10/15 = 2/3.
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