Q. 164.3( 7 Votes )

A hemispherical bowl of internal radius
9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

Answer :

Let n bottles are needed to empty the bowl,


Therefore,


Volume of bowl = Volume of 'n' bottles


For hemispherical bowl,


Radius, r = 9 cm


As we know,


Volume of a hemispherical bowl


Where r is the radius of hemisphere


Volume of bowl


For single cylindrical bottle,


Base radius, r = 1.5 cm


Height, h = 4 cm


As we know,


Volume of cylinder = πr2h


Where r is base radius,


h is height of cylinder.


Volume of one bottle = π(1.5)2(4) = 9π cm3


As,


Volume of bowl = volume of n bottles


486π = (9π)n



Hence, 54 bottles are needed to empty the bowl.


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