Hydrostatic force problem

1. A vertical plate consists of rectangular and semicircular portion and has dimensions as shown. It is submerged in a liquid such that the upper edge coincides with the free surface of the liquid. What is the ratio of L/R such that force on the rectangular portion is the same as that on the circular portion?











2. Relevant equations

F=γhA





3. The attempt at a solution



For rectangular part, since height of it is L and width of it is 2R

A=2R*L

h=L/2

so force on retangular part is

F_r=γ*2RL*L/2=γRL²



for semi circular portion

h=L+4R/3∏

A=∏R²/2

∴F_sc=γ(L+4R/3∏)*∏R²/2



Since F_r=F_sc



2RL²=(L+4R/3∏)∏R²(γ cancelled out)

.

.

L²=∏RL/2+2/3R²



now I'm stuck here. Am I doing this right? or did I misunderstand the problem?



English isn't my first language, so bear me.