1. **State the problem:** We have a cylindrical glass filled with juice to a height of 8 cm, and the volume of juice is 150 cm³. We need to find the radius $r$ of the glass. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Substitute known values:** $$150 = \pi r^2 \times 8$$ 4. **Isolate $r^2$:** $$r^2 = \frac{150}{8\pi}$$ 5. **Simplify the fraction:** $$r^2 = \frac{150}{8\pi} = \frac{\cancel{150}}{\cancel{8}\pi} \Rightarrow r^2 = \frac{75}{4\pi}$$ 6. **Calculate $r$ by taking the square root:** $$r = \sqrt{\frac{75}{4\pi}}$$ 7. **Evaluate numerically:** Using $\pi \approx 3.1416$, $$r = \sqrt{\frac{75}{4 \times 3.1416}} = \sqrt{\frac{75}{12.5664}} = \sqrt{5.966} \approx 2.44$$ 8. **Final answer:** The radius of the glass is approximately **2.44 cm**. **Note:** The second question about supermarket profit is not solved here as per instructions to solve only the first problem.