The formula for the lateral area of a cylinder refers to the calculation of the surface area of the cylinder’s side. A cylinder is a geometric shape consisting of two parallel circular faces and a curved surface connecting them. The lateral area of a cylinder specifically refers to the surface area of this curved side, excluding the surface areas of the cylinder’s base and top.

The formula for the lateral area of a cylinder is 2πrh. In this formula, r represents the radius of the cylinder’s base, and h represents the height of the cylinder.

The derivation of the formula 2πrh for the lateral area of a cylinder can be achieved by unfolding the cylinder’s side into a rectangle. Specifically, we can imagine the cylinder’s side being unfolded into a rectangle, with a length equal to the circumference of the circle, which is 2πr, and a width equal to the height of the cylinder, h. Therefore, the lateral area of the cylinder is equal to the area of the rectangle, which is 2πrh.

Related knowledge points to be learned include: “The formula for the area of a circle,” “The formula for the area of an ellipse,” “The formula for the surface area of a sphere,” “The formula for the area of an annulus,” “The formula for the surface area of a cylinder,” “The formula for the lateral area of a cylinder,” “The formula for the surface area of a cone,” and “The formula for the lateral area of a cone.”

It is worth noting that the formula for the lateral area of a cylinder only applies to cylinders that are not tilted. If a cylinder is tilted, a more complex formula will be required to calculate its lateral area.