Answer
$52266666.67 \ N$
Work Step by Step
The width of the dam at height $y$ is given by $w(y)=2 \sqrt {400-y^2}$
We need to use the formula for finding the total force on the dam such as: $F=\int_b^t \rho g (t-y) w(y) \ dy$.
Plug in the above formula the given values to obtain:
$W=\int_b^t \rho g (t-y) w(y) \ dy \\= 2 \times \int_{-20}^{0} \rho g (0-y) \sqrt {400-y^2} \ dy\\=2 \times (1000) (9.81) \times (\dfrac{8000}{3}) \\=52266666.67 \ N$
