The surface area formula of a cylinder is a formula for calculating the surface area of a cylinder. A cylinder is a geometric body consisting of two parallel circular faces and one side, whose surface area is the sum of the surface areas of the bottom, top and sides of the cylinder.

The formula for the surface area of the cylinder is 2πr(r+h), where r is the radius of the base of the cylinder and h is the height of the cylinder.

The derivation of this formula can be performed by expanding the cylinder into a rectangle. Specifically, we can expand the cylinder into a rectangle with a circumference of 2πr and a width of the height of the cylinder h. Therefore, the surface area of the cylinder is equal to the area of the rectangle plus the area of two circles, i.e. 2πr(r+h).

The steps for calculating the surface area of a cylinder are:

Here are three examples of using the cylindrical surface area formula:

1. If a cylinder has a base radius of 2cm and a height of 5cm, then its surface area is 2π(2)(2+5) + 2π(2)^2 = 52π ≈ 164cm^2.

2. A cylinder with a base radius of 3cm and a height of 8cm has a surface area of 2π(3)(3+8) + 2π(3)^2 = 94π ≈ 296cm^2.

3. If the base of a cylinder has a radius of 4cm and a height of 10cm, then its surface area is 2π(4)(4+10) + 2π(4)^2 = 120π ≈ 377cm^2.

Relevant knowledge points to learn: “The area formula of the circle” “the area formula of the ellipse” “The surface area formula of the ball” “The area formula of the circle” “the surface area formula of the cylinder” “The side area formula of the cylinder” “The surface area formula of the cone” “the side area formula of the cone”

It is important to note that the surface area formula for a cylinder only applies to a cylinder that is not tilted. If the cylinder is tilted, then a more complex formula is needed to calculate its surface area.