## Surface Area of a Cylinder

### Surface Area: Learn

Surface Area is the combined area of all two-dimensional surfaces of a shape.
Just like ordinary area, the units are the squares of the units of length
(that is, if a shape's sides are measured in meters,
then the shape's area is measured in *square meters*).

A cylinder has 2 circular surfaces (the *bases*) with a combined
area of 2*Π*r^{2}

A cylinder also has another surface, which, if rolled out, is a rectangle with one side measuring the height of the cylinder and the other side measuring the circumference of the base circles. That portion of the surface area, then, is 2*Π*r*h

So, all together, the formula for the surface area of a cylinder is

SA = 2*Π*r^{2} + 2*Π*r*h

For example, find the surface area of a cylinder with a height of 2m and a diameter of 6m.

First, we should note that we were given the diameter, but we need the radius for our formula. The radius r = 3 because the radius is exactly half of the diameter.

Then, we can substitute the known values into the formula, using 3.14 for Π:

SA = 2*Π*r^{2} + 2*Π*r*h

= 2*3.14*3^{2} + 2*3.14*3*2

= 56.52 + 113.04

= 169.56m^{2}

### Surface Area: Practice

#### Use 3.14 for pi.

00:00

What is the surface area of a cylinder whose

height = cm and

= cm?

cm^{2}

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