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 the diameter is same for both bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be 

Answer 1

let radius of hemisphere be R.

volume of hemisphere=2/3x22/7xR^3

Now, diameter of hemisphere=diameter of cylinder

So, radius of hemisphere = radius of cylinder=R.

it is written that radius is 50% more than height.

So, if height = h then radius can be written as h+1/2h= 3/2h.

So, R= 3/2h

Now, Volume of cylinder=22/7xR^2xh OR,

22/7x(3/2h)^2 x h

=22/7 x 9/4h^2 x h

=7.071 h^3