Confusion of circle and sphere for physics problems

[zabachi]

Homework Statement

The problem is attached

Homework Equations

P=F/A

The Attempt at a Solution

I did the question like this (got wrong answer though):

Surface area of sphere=4∏r²=4×∏×0.25²
Atmospheric pressure=1.01×10⁵

Force=1.01×10⁵×4×∏×0.25²≈80000N
Actual answer 20000N

So my friend said something about using a circle instead? I tried it and indeed got the right answer. So why do we use a circle's area instead of sphere.

 

[azizlwl]

Check the value of radius.

 

[zabachi]

i Changed the radius but the answer still reamins the same as i did the question previously itself

 

[Saitama]

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object.

The force is not completely perpendicular to the whole surface of hemisphere.

 

[Chestermiller]

You have to resolve the pressure force acting on each element of area of one of the hemispheres into the component in the direction that the rope is pulling. This is equivalent to using the projected area of the hemisphere times the atmospheric pressure.