The formula for the surface area of a cylinder is given by:
A = 2πr(h + r)
Where:
- A is the surface area
- r is the radius of the base of the cylinder
- h is the height of the cylinder
To break it down, a cylinder has two circular bases and a curved surface that connects them. The area of the circular bases can be calculated using the formula for the area of a circle, which is πr². Since there are two bases, this part contributes 2πr² to the total surface area.
The curved surface area can be viewed as a rectangle that wraps around the sides of the cylinder. Its height is h, and the length of this rectangle is equal to the circumference of the base (2πr). Thus, the area of the curved surface can be expressed as 2πrh.
Putting it all together, the total surface area is the sum of the area of the two bases and the curved surface area, leading to the final formula of A = 2πr(h + r).