## Surface Area of a Cone Lesson

### Cone Surface Area Formula

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

$$SA=\pi r(r+\sqrt{h^{2}+r^{2}})$$

Where *SA* is the surface area, *h* is the height of the cone, and *r* is the radius of the circle at the cone's base.

INTRODUCING

### Surface Area of a Cone Example Problems

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

#### Example Problem 1

Find the surface area of a cone with a height of 6 and a radius of 4.

Solution:

- We have both required dimensions to use the surface area formula.
- Plugging the height and radius in, we get:

SA = πr[r + √(h^{2}+ r^{2})]

SA = π(4)[4+ √(6^{2}+ 4^{2})] = π(4)[11.2111] = 140.883 **The surface area of the cone is 140.883.**

#### Example Problem 2

Find the surface area of a cone with a height of 1 and a radius of 1.

Solution:

- We have both required dimensions to use the surface area formula.
- Plugging the height and radius in, we get:

SA = πr[r + √(h^{2}+ r^{2})]

SA = π(1)[1+ √(1^{2}+ 1^{2})] = π(1)[2.414] = 7.584 **The surface area of the cone is 7.584.**