A spherical balloon has a surface area of 16 square inches, find the volume.
We are starting with the area and working backwards to the radius, and then go forward to find the volume.
We are given surface area.
Lets write down our formula.
The surface area equals 4pi radius squared
I know the surface area is 16 so I will plug it in.
Now I have to solve for r.
What is my first step?
Divide by 4, I need to get rid of that.
I now have 4=Pi r squared
I have the great circle but I need the radius.
I will divide by pi.
So I will take 4 and divide by pi.
4 divided by second function.
That gives me 1.2732 is equal to the radius squared
We take the square root to undo the square.
Square root of 1.27 = 1.13
So the radius = 1.13
We have gone backwards and taken the formula we know and worked back to the radius.
Now we will go forward again and take our volume formula
4/3 pi r cubed and plug in the radius of 1.13
4/3 times pi times 1.13 cubed.
Take 1.13 and cube it which is Math 3 and take that times 4 divided by 3 and it equals 1.923 pi and that is the volume of the sphere given the area.

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