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

The formula for the surface area of a cylinder is indeed represented as 2πrh + 2πr². This formula accounts for both the lateral surface area and the areas of the two circular bases of the cylinder.

To break it down, the lateral surface area (the curved surface that connects the two bases) is calculated as the circumference of the base (which is 2πr, where r is the radius) multiplied by the height (h). This gives you 2πrh.

In addition to this, there are two circular bases that contribute to the total surface area. The area of one base is πr²; therefore, the area of two bases is 2πr².

Combining these two components—lateral surface area and the area of the bases—results in the total surface area formula: 2πrh + 2πr².

This thorough approach highlights how each part of the cylinder contributes to the overall surface area.