Yin Yang

To simplify calculations, let the formula $f(d)$ of the area of a semicircle given diameter $d$ be $f(d)=cd^2$ for a constant $c$ .

We see that the area of the black region is $25c+9c-4c=30c$ and the area of the white region is $25c+4c-9c=20c$ .

Thus the ratio is $\dfrac{30c}{20c}=\dfrac{3}{2}$ so our answer is $3+2=\boxed{5}$ .

Let

$A_u$ = Area upper region

$A_l$ = Area lower region

$A_t$ = Total area

Assume the radius of the circle is $r = 10$ .

$A_u = \frac{5^2\pi}{2} - \frac{2^2\pi}{2} + \frac{3^2\pi}{2} = 15\pi$

$A_l = A_t - A_u = 5^2\pi - 15\pi = 10\pi$

$\frac{A_u}{A_l} = \frac{15\pi}{10\pi} = \frac{3}{2}$

$a + b = 3 + 2 =\boxed{5}$