jmc

We can set a proportion: $$\frac{AD}{AB}=\frac{3}{2}$$ We substitute $AB$ with 30 and solve for $AD$. $$\frac{AD}{30}=\frac{3}{2}$$ $$AD=45$$ We calculate the combined area of semicircle by putting together semicircle $AB$ and $CD$ to get a circle with radius $15$. Thus, the area is $225\pi$. The area of the rectangle is $30\cdot 45=1350$. We calculate the ratio: $$\frac{1350}{225\pi }=\frac{6}{\pi }\Rightarrow \boxed{6:\pi }$$ Note that we could have solved this without the measurement of $30$ inches.