Let’s start with the cylinder shape. If we flatten out a cylinder, we can see that it consists of two identical circles and a rectangle. The circles form the ends of the cylinder and the rectangle wraps around the circumference of the cylinder forming a curved surface. The formula for calculating the surface area incorporates these three shapes. First we need to establish the area of the two identical circles. As you already know, the formula for calculating the area of a circle is pi times r squared. But because there are two circles in a cylinder, we adjust the formula. So it becomes two times pi r squared.

Now the rectangle has a length of two times pi r because its length is equivalent to the circumference of the circle. R of course is the radius of the circle. The height of the rectangle is whatever the labelled height of the cylinder is. Our formula now looks like this, two times pi times r squared plus two times pi times r times h. Let’s apply the formula and calculate the surface area of this cylinder.

The cylinder has a labelled radius of two centimeters and a height of six centimeters. If we transfer these measurements into the formula, we have two times pi times two squared plus two times pi times two times six. This gives us two times three point one four times four plus two times three point one four times two times six. Work this out on the calculator and we get 25.12 plus 75.36 which equals 100.5 centimeters squared. Remember we’re still working with area. So the final answer must be shown in square units.