1. **State the problem:** We have a toy made from a cone and a hemisphere. Both have radius $r$ cm. The slant height of the cone is $3r$ cm. The total surface area of the toy is 304 cm². We need to find $r$. 2. **Formulas:** - Curved surface area of cone: $$A_{cone} = \pi r l$$ where $l$ is the slant height. - Curved surface area of sphere: $$A_{sphere} = 4 \pi r^2$$ - Since the hemisphere is half a sphere, its curved surface area is half of that: $$A_{hemisphere} = 2 \pi r^2$$ 3. **Calculate the total surface area:** The toy's total surface area is the curved surface area of the cone plus the curved surface area of the hemisphere (the base of the cone and hemisphere coincide, so the base area is not counted twice). $$\text{Total surface area} = A_{cone} + A_{hemisphere} = \pi r (3r) + 2 \pi r^2 = 3 \pi r^2 + 2 \pi r^2 = 5 \pi r^2$$ 4. **Set up the equation:** $$5 \pi r^2 = 304$$ 5. **Solve for $r^2$:** $$r^2 = \frac{304}{5 \pi}$$ 6. **Simplify and calculate $r$:** $$r = \sqrt{\frac{304}{5 \pi}}$$ 7. **Approximate the value:** Using $\pi \approx 3.1416$, $$r = \sqrt{\frac{304}{5 \times 3.1416}} = \sqrt{\frac{304}{15.708}} = \sqrt{19.35} \approx 4.4$$ **Final answer:** $$r \approx 4.4 \text{ cm}$$