Two circles and a rectangle combine to form a three-dimensional shape called a right circular cylinder (referred to from now on simply as a cylinder). The top and bottom of the cylinder are circles, while the middle of the cylinder is formed from a rolled-up rectangle, as shown in the diagram.
To determine the surface area of a cylinder, sum the areas of the three surfaces: The area of each circle is πr2, while the area of the rectangle is length × width.
Looking at the figure on the right, you can see that the length of the rectangle is equal to the circumference of the circle (2πr), and the width of the rectangle is equal to the height of the cylinder (h). Therefore, the area of the rectangle is 2πr × h. To find the total surface area (SA) of a cylinder, add the area of the circular top and bottom, as well as the area of the rectangle that wraps around the outside. To review:
| SA = 2 circles + rectangle = 2(πr2) + 2πrh |
The only information you need to find the surface area of a cylinder is 1) the radius of the cylinder, and 2) the height of the cylinder.