A hemispherical bowl is filled to the brim with a beverage. The contents of a bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be
- A66(2/3)%
- B78½%
- C100%Correct
- Dmore than 100% (that is, some liquid will still be left in the bowl)
Explanation
To find the correct answer, we compare the volumes of the hemispherical bowl and the cylindrical vessel.
Let the radius of both the bowl and the cylinder be r.
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Volume of the hemispherical bowl: The formula is 2/3 times pi times r cubed.
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Height of the cylinder: We are told the radius of the cylinder is 50 percent more than its height. This means r = 1.5h, or r = 3/2 times h. Rearranging this, the height h = 2/3 times r.
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Volume of the cylindrical vessel: The formula is pi times r squared times h. Substituting h = 2/3 times r into this formula, the volume becomes pi times r squared times 2/3 times r, which equals 2/3 times pi times r cubed.
Since the volume of the hemispherical bowl and the volume of the cylindrical vessel are both exactly 2/3 times pi times r cubed, the beverage will fill the cylinder perfectly. Therefore, the volume of the beverage in the cylindrical vessel is 100 percent.
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