1. **State the problem:** We need to find the radius $r$ of a cylindrical glass that holds 150 ml (which equals 150 cm³) of juice up to a height of 8 cm. 2. **Formula used:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute known values:** We know $V = 150$ cm³ and $h = 8$ cm, so $$150 = \pi r^2 \times 8$$ 4. **Isolate $r^2$:** $$r^2 = \frac{150}{8\pi}$$ 5. **Simplify the fraction:** $$r^2 = \frac{150}{8\pi} = \frac{\cancel{150}}{\cancel{8}\pi} \times \frac{1}{1} = \frac{75}{4\pi}$$ 6. **Calculate $r$ by taking the square root:** $$r = \sqrt{\frac{75}{4\pi}}$$ 7. **Evaluate numerically:** $$r = \sqrt{\frac{75}{4 \times 3.1416}} = \sqrt{\frac{75}{12.5664}} = \sqrt{5.966} \approx 2.44$$ 8. **Final answer:** The radius $r$ of the glass is approximately **2.44 cm**.