## Surface Area of a Sphere Lesson

### Sphere Surface Area Formula

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

**SA = 4πr ^{2}**

Where *SA* is the surface area and *r* is the radius of the sphere.

INTRODUCING

### Surface Area of a Sphere Example Problems

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

#### Example Problem 1

Find the surface area of a sphere with a radius of 10.

Solution:

- Plugging what we know into the surface area formula, we get:
- SA = 4πr
^{2} - SA = 4π(10
^{2}) = 400π **The surface area is 400π.**

#### Example Problem 2

The surface area of a sphere is measured to be 100π square meters. What is the diameter of the sphere in meters?

Solution:

- First, we will plug the surface area value into the formula and solve for the radius
*r*. - SA = 4πr
^{2} - 100π = 4πr
^{2} - 25 = r
^{2} - r = 5
- Now that we have the radius, let's convert it to diameter.
- d = 2r
- d = 2(5) = 10
**The diameter of the sphere is 10 meters.**