1. **State the problem:** Calculate the surface area and volume of a composite shape made of two cylinders: a larger cylinder with diameter 4.0 cm and height 1.5 cm, and a smaller attached cylinder (rod) with diameter 1.0 cm and length 4.5 cm. 2. **Formulas:** - Volume of a cylinder: $$V = \pi r^2 h$$ - Surface area of a cylinder (excluding bases): $$A_{side} = 2 \pi r h$$ - Total surface area of a cylinder: $$A = 2 \pi r h + 2 \pi r^2$$ 3. **Calculate volumes:** - Larger cylinder radius: $$r_1 = \frac{4.0}{2} = 2.0\text{ cm}$$ - Smaller cylinder radius: $$r_2 = \frac{1.0}{2} = 0.5\text{ cm}$$ - Volume of larger cylinder: $$V_1 = \pi (2.0)^2 (1.5) = \pi \times 4 \times 1.5 = 6\pi\text{ cm}^3$$ - Volume of smaller cylinder: $$V_2 = \pi (0.5)^2 (4.5) = \pi \times 0.25 \times 4.5 = 1.125\pi\text{ cm}^3$$ - Total volume: $$V = V_1 + V_2 = 6\pi + 1.125\pi = 7.125\pi \approx 22.37\text{ cm}^3$$ 4. **Calculate surface areas:** - Surface area of larger cylinder: $$A_1 = 2 \pi (2.0)(1.5) + 2 \pi (2.0)^2 = 6\pi + 8\pi = 14\pi\text{ cm}^2$$ - Surface area of smaller cylinder: $$A_2 = 2 \pi (0.5)(4.5) + 2 \pi (0.5)^2 = 4.5\pi + 0.5\pi = 5\pi\text{ cm}^2$$ 5. **Adjust for the attached base:** The smaller cylinder is attached to the larger one, so one base of each cylinder is not exposed. - Subtract one base area of the smaller cylinder: $$\text{Base area} = \pi (0.5)^2 = 0.25\pi$$ - Subtract one base area of the larger cylinder where the smaller cylinder attaches: $$\text{Base area} = \pi (0.5)^2 = 0.25\pi$$ 6. **Total surface area:** $$A = A_1 + A_2 - 2 \times 0.25\pi = 14\pi + 5\pi - 0.5\pi = 18.5\pi \approx 58.12\text{ cm}^2$$ **Final answers:** - Volume: $$\boxed{22.37\text{ cm}^3}$$ - Surface area: $$\boxed{58.12\text{ cm}^2}$$