fluids mechanics...

Horizontal Force acting will be independent fo the shape of the body..
It will depend only on the depth of the body. (This is a very strange comment to make to start with but can be verified by taking an element of any slope at a particular depth)

So what you will need to do is to find the total force take P(h).dh ... where P(h) is the pressure at height h

This will be ∫ρgh dh = ρgh²/2

Again, you have two sides.. the net horizontal force should be the same...

so (2ρ)gh²/2=3ρg(r)²/2

Hence the answer...

I have still not proved the first part which needs to be proved.. (and is a easy one if you dont fear taking elements and I leave that to you as an exercise)