Surface Area of Spheres - Concept
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.
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.