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## Functions

Current time:0:00Total duration:2:13

# Function notation example

## Video transcript

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 pi r cubed, 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 pi r cubed. 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 of-- that's not
the same color. We do it in that brownish
color right over here. So V of 3 is equal to 4/3
pi-- and instead of r cubed, I would write 3
cubed-- 4/3 pi 3 cubed. This is how the function
definition works. Whatever we input
here, it will replace the r in the expression. So V of 3 is going to
be equal to-- so this is going to be equal to 4/3 pi
times-- 3 to the third power is 27. 27 divided by 3 is
9, so this is 9. 9 times 4 is 36 pi. So this is equal to 36 pi. And since this was
in inches, our volume is going to be in inches
cubed or cubic inches. So that's the volume
of water that Frank can put in the balloon--
36 pi cubic inches.