The surface area of a right cylinder is the total area of all its curved and flat surfaces. It can be calculated using the following formula:

Surface Area = 2πr(h + r)

Where r is the radius of the circular base of the cylinder, and h is its height.

To visualize this, imagine a soda can. The curved part of the can is the lateral surface area, while the top and bottom circular parts are the base areas. To find the total surface area of the can, you would need to add the lateral surface area to the two base areas.

Another example of a right cylinder could be a pipe or a drum. The surface area of the cylinder is important to know in manufacturing, as it helps determine the amount of material needed to construct the cylinder. It is also important in engineering and architecture for calculating the heat transfer, pressure, and fluid dynamics of cylindrical structures.

The formula for determining the surface area of a right cylinder is defined as: