## Surface Area of a Cylinder Lesson

### Cylinder Surface Area Formula

The formula for surface area of a cylinder is given as:

**SA = 2πrh + 2πr ^{2}**

Where *SA* is the surface area, *r* is the radius of the base circle, and *h* is the height of the cylinder.

INTRODUCING

### Surface Area of a Cylinder Example Problems

Let's go through a couple of example problems together to practice finding the surface area of a cylinder.

#### Example Problem 1

What is the surface area of a cylinder with a diameter of 20 and a height of 20?

Solution:

- Let's convert diameter to radius. D = 2r, 20 = 2r, so r = 10.
- Now let's plug the radius and height into the surface area formula.
- SA = 2πrh + 2πr
^{2} - SA = 2π(10)(20) + 2π(10
^{2}) = 2π(200) + 2π(100) - SA = 1,884.956
**The surface area is 1,884.956.**

#### Example Problem 2

A cylinder is measured to have a surface area of 24 square meters. It's height and radius are equal. What is the height of the cylinder?

Solution:

- Let's set up relations between height and radius that we can substitute into the formula.
- h = r
- rh = h
^{2} - r
^{2}= h^{2} - Now let's plug what we know into the surface area formula and solve for h.
- SA = 2πrh + 2πr
^{2} - 24 = 2πh
^{2}+ 2πh^{2} - 24 = 4πh
^{2} - 1.910 = h
^{2} - h = 1.382
**The height of the cylinder is 1.382 meters.**