Question

A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of the
cylinder is 20 cm.  

Answer 1

 
Let the height of the water level be 'h', after the solid is turned upside down. 

Volume of water in the cylinder 

= `pi(7/2)^2 10` 

Volume of the hemisphere 

= `2/3pi(7/2)^3 ` 

Volume of water in the cylinder

= Volume of water level − Volume of the hemisphere  

`pi(7/2)^2 10 = pi(7/2)^2h - 2/3pi(7/2)^2` 

`=> 10 = h - 7/3` 

`=> h = 10 + 7/3`

`=> h = 12 1/3 cm`  

The height of water when the hemisphere is facing downwards is `12 1/3 cm`