Surface Area


Have you ever wanted to gift wrap a poster tube? Did you ever wonder how much wrapping paper you would need? Let's explore the formula.

Surface Area of a Cylinder = 2 Π r2 + 2 Π r h
h = height of the cylinder, r = radius of the top, approximate value of pi: 3.14.

Similar to the rectangle we just finished,
Surface Area = Areas of top and bottom + Area of the side(s)

Unlike the rectangle, which has 4 sides, the cylinder only has 1 side.

Let's picture our cylinder-shaped gift. The surface area is the areas of all the parts needed to cover the can, which are the top and bottom circles and the rectangular paper label that folds around the middle.

Circle area formula is Π r2. Since there is both a top and a bottom, that gets multiplied by two.

Let's use another example, a soup can. The side is like the paper label of a soup can. When you peel it off and lay it flat, it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, also known as the circumference of a circle. Since the label wraps once around the can, the area of the rectangle is the circumference of the circle x height or (2 Π r) * h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(Π r2) + (2 Π r) * h

Although Π is approximately 3.14, in this activity we will use
Π = 3.14 for calculations.

3D cylinder with radius and height labeled
Flattened cylinder with radius and height labeled

Surface Area of a Cylinder
After hitting the next button, enter your calculation in the box. Upon hitting the enter key, if your calculation is wrong, your answer will appear in red and you will be given two hints.