On what area is the pressure of the gas acting?

[Asad Raza]

Hi
I was perplexed as to why the area on which the pressure acts is 'piR^2'. Since one complete half of the sphere is in contact with the gas, hence the pressure should be 4piR^2/2 (half of the surface area of sphere i.e 2piR^2)

 

[Vishal Mishra]

Yes you are right pressure acts on half of the sphere and you also know pressure always acts perpendicular to the area so you can imagine how the pressure is acting on the sphere now you might observe if you try to resolve pressure into horizontal and vertical components the net pressure is only in vertical direction since it is mathematically cumbersome to resolve all those pressure lines in this given problem the area of the sphere has been resolved .