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Question

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If he diameter is same for both the bowl and the cylinder, then the amount of the beverage that can be poured from the bowl into the cylindrical vessel is __________.

A
6623%
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B
7812%
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C
100%
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D
None of these
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Solution

The correct option is C 100%
We know that radius of both hemisphere and cylinder is same.
Let it be r

radius(r) of cylinder is 50% more than its height(h)
r =h+12h

h=23r
Now,
We know,
Volume of cylinder =πr2h
=πr2(23r)=23πr3

Volume of hemisphere =23πr3

Volume of both cylinder and hemisphere are equal.
100% liquid can be transfered.

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