1. **State the problem:** We need to find the total surface area of a cylinder given its net. 2. **Identify the parts of the net:** The net consists of a rectangle and two circles. - The rectangle represents the lateral surface area. - Each circle represents one base of the cylinder. 3. **Given dimensions:** - Radius of each circle $r = 3$ cm - Height of the rectangle (cylinder height) $h = 5$ cm - Length of the rectangle (circumference of the base) $= 6\pi$ cm 4. **Formulas:** - Lateral surface area $= 2\pi r h$ - Area of one base $= \pi r^2$ - Total surface area $= \text{lateral area} + 2 \times \text{base area}$ 5. **Calculate lateral surface area:** $$ 2\pi r h = 2\pi \times 3 \times 5 = 30\pi $$ 6. **Calculate area of one base:** $$ \pi r^2 = \pi \times 3^2 = 9\pi $$ 7. **Calculate total surface area:** $$ 30\pi + 2 \times 9\pi = 30\pi + 18\pi = 48\pi $$ **Final answer:** The total surface area of the cylinder is $48\pi$ square centimeters.