1. **State the problem:** We have a cylinder net consisting of two circles each with radius 5 mm and a rectangle with height 3 mm and length $x$. 2. **Find the length $x$:** The length $x$ of the rectangle corresponds to the circumference of the circular base of the cylinder. Formula for circumference of a circle: $$C = 2\pi r$$ where $r$ is the radius. Given $r = 5$ mm: $$x = 2\pi \times 5 = 10\pi$$ 3. **Find the total surface area of the cylinder:** The total surface area $A$ is the sum of the areas of the two circles and the rectangle. Area of one circle: $$A_{circle} = \pi r^2 = \pi \times 5^2 = 25\pi$$ Area of two circles: $$2 \times 25\pi = 50\pi$$ Area of the rectangle (side surface): $$A_{rect} = x \times h = 10\pi \times 3 = 30\pi$$ Total surface area: $$A = 50\pi + 30\pi = 80\pi$$ **Final answers:** - Length $x = 10\pi$ mm - Total surface area $= 80\pi$ mm$^2$