Surface Area of a Sphere

There comes a time in a person's life when they realize something is missing...and oftentimes, they come to realize that it is because they do not know how to calculate the surface area of a sphere!

Alright, maybe not. Chances are, unless you are in some very specialized field, you will not need this on a daily basis. But you will, however, need it for math classes.

So, without further ado, I will proceed to explain how this fun and mysterious procedure is carried out.

Step 1 Deconstructing the Sphere

A sphere is a bit like a super-circle...you can rotate a circle around its center in any direction and it will trace the outline of the sphere. As a result, it should make sense that the formula to find the surface area of a sphere is very closely related to that of the one to find the circumference of a circle.

As is shown in the first picture below, the formula for the circumference of a circle is 2(pi)(r). The second one shows how similar the sphere formula is, being 4(pi)(r)². Why is the formula in this format? The answer lies in radian measurement.

If you are not familiar with radian measures, you will encounter them in trigonometry at the latest. Many people learn about them in high school Algebra 2, but they are not explained very well and so they seem a bit mysterious.

The next step will be a very basic description of how radian measurement works as relates to these formulas. If you are already familiar with them, or don't want the theory, by all means skip ahead.

Comments

[james.mcglashan]

I get it but it is 3D so easy to understand but I dont really see how this will come up in life please explain when.

[thepelton]

Another definition of PI is 22/7. Yes, I know it isn't exactly the same, but for calculations smaller than an american basketball, it will do.

[Terry2030]

Oops I missed it somewhere. Your formula starts with 4. Where did you get that number ? It is probably there in your Instructable and I just missed it. But help me out here. I think your Instructable is great.

[tommylovesjamie]

I hate to do this to an excellent math instructable, but you could probably benefit from avoiding the tendency to call pi "3.14". I don't agree with the estimate, and if you use a calculator for your work, it should have its own value for pi to a much higher degree of accuracy. aside from that, I really do love the job you have done.

[victus_maestro]

I know what you mean, it's definitely a difficult balance to strike between brevity and specificity. I haven't really aimed to target a specific level of math learner, and generally the higher you go, the more precise your calculations will be, so 2 digits is by no means universally sufficient. Whenever possible, I would definitely agree with using the calculator's pi for much greater precision. Thanks for the advice and support!