# Surface Area of Spheres - Concept

###### Explanation

In general, surface area is the sum of all the shapes that cover the surface of an object. To calculate the **surface area of a sphere** we multiply 4 by pi by the radius of the sphere squared. Given this formula, we can find the surface area of a sphere when given the radius. Similarly, we can find the radius of a sphere is we are given the surface area. This formula is very similar to other prism volume formulas.

###### Transcript

When we're talking about the surface area of the sphere, you can think of it as how much paint would you need to cover a tennis ball or if you'd looked at a baseball and you took all the stitching apart, how much leather would you need to make that ball?

Well, to find the surface area of a sphere, you're going to use the formula that surface area equals 4 times pi times the radius squared. Now, notice the dimensionality here. We have r to the second power which agrees with what we know about surface area which is it's a two dimensional property. So the only thing that you need to know in order to calculate the surface area of a sphere is this formula 4 times pi times the radius squared. Let's look at a very basic example of this application.

If the radius of a sphere is 3 centimetres, what is the surface area? Well we'll start off by writing our surface area formula. Surface area equals 4 pi r squared and then we'll say our radius is 3 centimetres. So then we just need to substitute in and we'll know our surface area.

We'll say that surface area is equal to 4 times pi times 3 squared. 3 squared we know is 9, 9 times 4 is 36. So the surface area of that sphere is going to be 36 pi square centimetres. So when you have a surface area problem and they tell you the radius, all you need to do is to substitute into your formula and simplify.