Volume of a Sphere

Find the volume of a sphere with
a diameter of 14 centimeters.

So if I have a sphere-- so
this isn't just a circle,

this is a sphere.

You could view it as
a globe of some kind.

So I'm going to shade
it a little bit so you

can tell that it's
three-dimensional.

They're giving us the diameter.

So if we go from one
side of the sphere

straight through
the center of it.

So we're imagining that we
can see through the sphere.

And we go straight
through the centimeter,

that distance right over
there is 14 centimeters.

Now, to find the volume of a
sphere-- and we've proved this,

or you will see a proof for this
later when you learn calculus.

But the formula for
the volume of a sphere

is volume is equal
to 4/3 pi r cubed,

where r is the
radius of the sphere.

So they've given
us the diameter.

And just like for circles,
the radius of the sphere

is half of the diameter.

So in this example, our radius
is going to be 7 centimeters.

And in fact, the sphere
itself is the set

of all points in three
dimensions that is exactly

the radius away from the center.

But with that out of
the way, let's just

apply this radius being 7
centimeters to this formula

right over here.

So we're going to
have a volume is

equal to 4/3 pi times 7
centimeters to the third power.

So I'll do that in
that pink color.

So times 7 centimeters
to the third power.

And since it
already involves pi,

and you could
approximate pi with 3.14.

Some people even
approximate it with 22/7.

But we'll actually just
get the calculator out

to get the exact
value for this volume.

So this is going to
be-- so my volume is

going to be 4 divided by 3.

And then I don't want
to just put a pi there,

because that might interpret
it as 4 divided by 3 pi.

So 4 divided by 3 times pi,
times 7 to the third power.

In order of operations,
it'll do the exponent

before it does the
multiplication,

so this should work out.

And the units are going to be
in centimeters cubed or cubic

centimeters.

So we get 1,436.

They don't tell us
what to round it to.

So I'll just round it to
the nearest 10th-- 1,436.8.

So this is equal to
1,436.8 centimeters cubed.

And we're done.