Sphere Surface Area Formula

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

SA = 4πr²

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

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:

1. Plugging what we know into the surface area formula, we get:
2. SA = 4πr²
3. SA = 4π(10²) = 400π
4. 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:

1. First, we will plug the surface area value into the formula and solve for the radius r.
2. SA = 4πr²
3. 100π = 4πr²
4. 25 = r²
5. r = 5
6. Now that we have the radius, let's convert it to diameter.
7. d = 2r
8. d = 2(5) = 10
9. The diameter of the sphere is 10 meters.