2πrh + 2πr^2

The expression 2πrh + 2πr^2 represents the formula for the surface area of a cylinder. To understand this formula and how to calculate the surface area, let's break it down step by step.

A cylinder is a geometric shape with two circular bases and a curved surface connecting them. The formula for the surface area of a cylinder consists of two parts:

1. The first term, 2πrh, represents the area of the curved surface, also known as the lateral surface area. It is calculated by multiplying the circumference of the base, which is 2πr (where r is the radius), by the height of the cylinder, h.

2. The second term, 2πr^2, represents the sum of the areas of the two circular bases. Each base has an area of πr^2 (where r is the radius), so we multiply it by 2 to account for both the top and bottom bases.

By adding both terms together, we get the total surface area of the cylinder. This formula allows us to find the amount of surface area that would be covered if we were to unwrap the cylinder and lay it flat.

To use this formula to calculate the surface area of a cylinder, you need to know the values for the radius (r) and height (h). Plug in these values into the formula and perform the calculations to find the result.