1. **State the problem:** We need to find the exact 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 of the cylinder. - Each circle represents one base of the cylinder. 3. **Given dimensions:** - Radius of each circle (base) $r = 2$ cm - Length of the rectangle (height of the cylinder) $h = 7$ cm 4. **Formula for surface area of a cylinder:** $$S_A = 2\pi r^2 + 2\pi r h$$ - $2\pi r^2$ is the area of the two circular bases. - $2\pi r h$ is the lateral surface area (rectangle). 5. **Calculate each part:** - Area of bases: $$2\pi (2)^2 = 2\pi \times 4 = 8\pi$$ - Lateral area: $$2\pi (2)(7) = 28\pi$$ 6. **Add the areas:** $$S_A = 8\pi + 28\pi = 36\pi$$ 7. **Final answer:** The exact surface area of the cylinder is **$36\pi$ cm$^2$**.