1. **Problem statement:** Find the surface area and volume of a composite solid consisting of a cylinder with a hemispherical top. The radius $r$ is 3 in and the cylinder height $h$ is 12 in. 2. **Formulas:** - Surface area of cylinder (without top): $A_{cyl} = 2\pi r h$ - Surface area of hemisphere: $A_{hem} = 2\pi r^2$ - Total surface area = lateral area of cylinder + surface area of hemisphere (no base of cylinder counted because hemisphere covers it) - Volume of cylinder: $V_{cyl} = \pi r^2 h$ - Volume of hemisphere: $V_{hem} = \frac{2}{3} \pi r^3$ - Total volume = volume of cylinder + volume of hemisphere 3. **Calculate surface area:** - Cylinder lateral area: $2\pi (3)(12) = 72\pi$ - Hemisphere surface area: $2\pi (3)^2 = 18\pi$ - Total surface area: $72\pi + 18\pi = 90\pi$ - Approximate: $90\pi \approx 90 \times 3.1416 = 282.74$ in² 4. **Calculate volume:** - Cylinder volume: $\pi (3)^2 (12) = 108\pi$ - Hemisphere volume: $\frac{2}{3} \pi (3)^3 = \frac{2}{3} \pi 27 = 18\pi$ - Total volume: $108\pi + 18\pi = 126\pi$ - Approximate: $126\pi \approx 126 \times 3.1416 = 395.84$ in³ 5. **Final answers:** - Surface area $\approx 282.74$ in² - Volume $\approx 395.84$ in³ Note: The volume matches the given value 395.83 in³, confirming correctness.