Answer:
By 300 %
Explanation:
Let's start defining the cuboidal tank dimensions.
Their three dimensions are the same because its cuboidal ⇒
Tank volume = [tex](h).(h).(h)=h^{3}[/tex]
Let's also define :
ρ = water density
g = gravity
The water hydrostatic force per unit width on a vertical side is
F = ρ.g.[(water height)^2].(1/2)
When the tank is half filled with water the force is (in the following equations I replace ρ.g by R):
[tex]F1=R.(\frac{h}{2})^{2}.\frac{1}{2}\\F1=R.\frac{h^{2}}{8}[/tex]
When the tank is completely filled the force is (remember that ρ.g = R):
[tex]F2=R.h^{2}.\frac{1}{2} \\F2=R.\frac{h^{2}}{2}[/tex]
The force increased percently by :
[tex]\frac{F2-F1}{F1}.100=\\[/tex]
[tex]F2-F1=R.\frac{h^{2}}{2}-R.\frac{h^{2}}{8}=\frac{3}{8}.R.h^{2}[/tex]
[tex]\frac{F2-F1}{F1}=\frac{\frac{3}{8}.R.h^{2}}{\frac{R.h^{2}}{8}}=3[/tex]
[tex]\frac{F2-F1}{F1}.100=3.(100)=300[/tex]
The percent is 300 %
