jmc

We can begin by calculating the volume of the liquid in the glass. Since the glass is half full, the portion filled with liquid has height 3 inches. The volume will be $\pi r^{2}h=\pi \cdot 1^2\cdot 3=3\pi$. Now, since the ratio of lemon juice to water is 1:11, the ratio of lemon juice to the liquid will be 1:(1+11) which is 1:12. So, the volume of lemon juice in the glass is: $$3\pi \cdot \frac{1}{12}=\frac{\pi }{4}\approx .7854$$ So, the answer is $\boxed{.79}$ to the nearest hundredth.