Chapter 8.3, Problem 20E

(a) Use the formula of Exercise 18 to show that

$F=\left(\rho g\bar{x}\right)A$

where $\bar{x}$ is the x-coordinate of the centroid of the plate and A is its area. This equation shows that the hydrostatic force against a vertical plane region is the same as if the region were horizontal at the depth of the centroid of the region.

(b) Use the result of part (a) to give another solution to Exercise 10.