1. The problem is to find the surface area of a cylinder given the net dimensions: radius $r=9.5$ mm and height $h=17$ mm. 2. The formula for the surface area of a cylinder is $$\text{Surface Area} = 2\pi r^2 + 2\pi rh$$ where: - $2\pi r^2$ is the combined area of the two circular bases. - $2\pi rh$ is the area of the rectangular side (the lateral surface). 3. Calculate the area of the circles: $$2\pi r^2 = 2 \times \pi \times (9.5)^2 = 2 \times \pi \times 90.25 = 180.5\pi$$ 4. Calculate the area of the rectangle: $$2\pi rh = 2 \times \pi \times 9.5 \times 17 = 323\pi$$ 5. Add the two parts to find the total surface area: $$\text{Surface Area} = 180.5\pi + 323\pi = 503.5\pi$$ 6. Approximate using $\pi \approx 3.1416$: $$503.5 \times 3.1416 \approx 1581.36$$ mm$^2$ 7. Rounded to the nearest integer, the surface area is: $$1581$$ mm$^2$ Final answer: The surface area of the cylinder is approximately $1581$ mm$^2$.