Introduction: Surface Area of a Sphere

Wahoo! Fun algebraic formulas...I know...I'm a nerd. Well, the exciting expression for this one is...(drum-roll please)...4 (pi) r 2.

Sounds Easy Enough...And don't worry...If you don't know what this means were going to go through all of this...(Oh and if you're worse than me with nerdiness-I'm going to explain how we got this formula)

Ok say that you own a snow ball shop and you sell snow balls (hypothetically of course) Well, you have noticed that when you put the snow ball in the freezer and come back the next morning and they look smaller, well, if you find the surface area of both times and take the difference...What if they're getting smaller!!!!...Oh my God...this is an outrage. Solution: turn down the temperature

So mayyyybe you might not have to use this situation but you get my point.

Maybe you just want to know what the surface area of a basketball is...Well, the radius is about 4 inches. Read the rest of this Instructable and find out the surface area

Step 1: Parts of This Formula


Learning with Diagrams

Think of this as more of those acrostic's more fun that way

Step 2: If You Know the Radius...You Have Come to the Right Place

Cheezy title...I know

So what we want to do is simplify the formula. Let's say that our diameter is 10. The radius is half of the diameter making the radius..."5". Now, were gonna put the five in for the "r" (which stands for radius) Our formula is now:

4 (pi) (52)

The "2" tells us that we need to times the number before it twice:

4 (pi) (5*5) = 4 (pi) 25

That shortens our formula...but we can get even smaller...Let's times "pi" and "4" together. We're gonna shorten pi to its second decimal point:

4*3.14 (25) = (12.56) (25)

Note: Everytime you do this formula...the 12.56 will always be the same

Now we have two numbers right by each other...There's nothing left to do now but to multiply


Congratulations...We have just calculated our first surface area

But hold on...There's a twist...Say you have the surface area but don't have the radius
Go to the next step to find out what to do

Step 3: Reversing the Action

Now say we have the surface area-("1000") and we need to find the radius. This is what we got to do.

Before we move on, check out the formula down below...Study it...Lodge it into your brain...Make sure you can recite it back to your sleep...hopping on one foot...while burping...and wearing an eye patch because you went cow tipping and the cow fought back. If you can do that you're ready to move on...If not, I'll wait.
>>>>> In words, the formula is radius is equal to the square root of the dividend of the surface >>>>> area and the quotient of 4 and pi
Took you long enough. Ok back to business.
We know the surface area, "1000", and we know pi*4=12.56

So we have to take the 1000 and divide it by 4(pi):


So now we take our new answer (79.61) and find the square root for that:


And there we go...Our radius is "8.92"
Wahoo...Now go around and show everyone your knowledge. Hehe

Optional: To find out how and why we have our original formula...Go to the next step

Step 4: Why...Why...Why

Oh I'll tell you why

Oh wait no I won't I'm too tired just go to

it's a great site to learn from.

Step 5: Too Lazy...Here Is How to Make an Excel Spreadsheet to Do All the Work

If you know the RADIUS
1. Open excel
2. Click in B1
3. Type in =A1*A1*3.14*4
4. Type in your radius in cell A1
5. Press Enter and B1 should give you you're answer

Now if you know the SURFACE AREA
1. Open excel
2. Click in B1
3. Type in =SQRT(A1/12.56)
4. Type in your surface area in cell A1
5. Press Enter and B1 should give you you're answer

Nothing fancy but it gets the job done

Oh and one last thing...Thanks for reading this and you are officially (well, declared by me) a surface area of sphere master

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