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A hemispherical bowl is filled to the rim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is

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66.66 %

78.50 %

m o r e t h a n 100 %

100 %

answer is C.

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Detailed Solution

Let the height of the vessel be $h$ m

Radius of the bowl $= \frac{h}{2} m$

Volume of the vessel $= π {(\frac{h}{2})}^{2} \times h = \frac{1}{4} π h^{3}$

As the volume of the vessel is 3 times more than that of the bowl, it can contain $100 %$ of the beverage

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