What is the formula for the surface area of a cylinder?

The surface area of a cylinder can be found by considering both the lateral surface area and the area of the two circular bases. The lateral surface area (the area around the sides of the cylinder) is calculated using the formula 2 times pi times radius times height. This represents the area of the rectangle that wraps around the cylinder when unrolled.

The area of each circular base is calculated using the formula pi times radius squared, and since a cylinder has two bases, you multiply this area by 2. Therefore, the total surface area of the cylinder combines the lateral surface area with the area of both bases.

The correct formula for the total surface area of a cylinder is therefore written as:

Total Surface Area = Lateral Surface Area + Area of Bases

= (2 * pi * radius * height) + (2 * pi * radius^2)

= 2 * pi * radius * (height + radius)

This shows that option B, which represents the sum of the height and radius, captures the full surface area by including the contributions from both the lateral area and the bases.

Understanding this formula helps in applying it to real-world scenarios, such as calculating the surface area needed for material when wrapping a cylindrical object or calculating paint coverage on a