Final answer:
The surface area of a cylinder is calculated by combining two times the area of its circular bases with the area of the rectangle formed by the unrolled curved surface. The formula is SA = 2πr² + 2πrh, wherein 'r' is the radius and 'h' is the height of the cylinder. It's important to round the result to the appropriate number of significant figures.
Step-by-step explanation:
The surface area of a cylinder can be calculated by combining the areas of its two circular bases with the area of the rectangle that would be formed if the curved surface of the cylinder were 'unrolled' into a flat shape. To do this, first calculate the area of one of the circular bases using the formula A = πr², where 'A' is the area and 'r' is the radius of the base. Since the cylinder has two bases, you will multiply this area by 2. Next, find the area of the rectangle, which is the lateral surface, by multiplying the circumference of the base (which is 2πr) by the height 'h' of the cylinder. Thus, the full formula for the surface area (SA) of the cylinder becomes:
SA = 2πr² + 2πrh.
Remember to keep the significant figures in mind when doing calculations, as they determine the precision of your answer. Using a calculator with eight-digit output might give you a very precise number, but if the radius is given to only two significant figures, you should round the calculated area accordingly.