Final answer:
The surface area of a cylinder with one end is the sum of the area of the single circular base and the area of the side, given by the formula Surface Area = πr² + 2πrh.
Step-by-step explanation:
The surface area of a cylinder with one end can be calculated by combining elements of both circular and rectangular geometries. Typically, the total surface area of a closed cylinder includes the areas of both circular ends plus the area of the rectangle formed by 'unrolling' the side of the cylinder.
\However, for a cylinder with only one end, the surface area would be the area of a single circular end (πr²), where π is Pi and r is the radius of the circular base, plus the area of the rectangle formed by the side of the cylinder (2πrh), where h is the height of the cylinder.
To calculate the surface area for this cylinder with one end open, you therefore add the area of the single circular base (πr²) to the area of the side (2πrh), so the formula becomes Surface Area = πr² + 2πrh.