Transcription
Frank wants to fill up a spherical water balloon with as much water as possible. The balloons he bought can stretch to a radius of 3 inches--not too big. If the volume of a sphere is--and this is volume as a function of radius--is equal to 4/3 πr³, what volume of water in cubic inches can Frank put into the balloon?
So this function definition is going--if you give it a radius in inches, it's going to produce a volume in cubic inches. So let's rewrite it. Volume as a function of radius is equal to 4/3 πr³. Now, they say the balloons he bought can stretch to a radius of 3 inches. So let's think about, if the radius gets to 3 inches, what the volume of that balloon is going to be.
So we essentially would just input 3 inches into our function definition. So everywhere where we see an r, we would replace it with a 3. So we could write--and just to be clear, let me rewrite it in the same color. V(3) is equal to 4/3 π--and instead of r³, I would write 3³--4/3 π3³. This is how the function definition works. Whatever we input here, it will replace the r in the expression.
So V(3) is going to be equal to--so this is going to be equal to 4/3 π times--3 to the third power is 27. 27 divided by 3 is 9, so this is 9. 9 times 4 is 36π. So this is equal to 36π. And since this was in inches, our volume is going to be in inches³ or cubic inches. So that's the volume of water that Frank can put in the balloon--36π cubic inches.