(Solved): The figure to the right shows the shape and dimension of a small dam. Assuming the water level is a ...

The figure to the right shows the shape and dimension of a small dam. Assuming the water level is at the top of the dam and that the shape of the dam is a semicircle, find the total force on the face of the dam. Use $1000\mathrm{kg}/{\mathrm{m}}^3$ for the density of water and $9.8\mathrm{m}/{\mathrm{s}}^2$ for the acceleration due to gravity. Find the width function $w(y)$ for each value of $y$ on the face of the dam. In this case, choose an origin so that $y=0$ is the middle of the top of the tank, and a $y$-value of the negative radius of the semicircle is the bottom of the tank. Choose the correct answer below. A. $w(y)=2\sqrt{y^2-81}$ B. $w(y)=2\sqrt{81-y^2}$ C. $w(y)=2\left(y^2-81\right)$ D. $w(y)=2\left(81-y^2\right)$ Set up the integral that should be used to find the total force on the face of the dam. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) A. $\int 1dx$ B. $\int (s)dy$