We want to find the volume of the sphere
with diameter of 27 centimeters
for us to find the exact volume,
then the volume rounded to two decimal places.
When we think of a sphere,
we can think of a ball as we see pictured here.
But it's really a three-dimensional surface,
where every point on the surface
is equidistant from a point,
which would be the center.
The distance from the center to the surface,
this distance here,
would be the radius.
But notice how in this example we're given the diameter,
which should be the segment passing through the center
with two endpoints on the surface.
So, the diameter would be this distance here.
Notice how the radius is equal to half of the diameter.
And looking at our volume formulas,
here's the volume formula for a sphere.
Volume is equal to 4/3 pi r cubed.
So, to begin, let's find the radius.
The radius is going to be equal to half of the diameter,
where, again, the diameter is 27 centimeters.
So we have 27 centimeters divided by two.
Let's go and leave this in fraction form,
because notice how there's already
a fraction in our formula.
So leave this as 27/2 centimeters.
And now we can find the volume.
The volume is going to be equal to 4/3
times pi
times r cubed.
Let's leave the units off,
and just remember that the units will be cubic centimeters.
So we'll have 27/2 cubed.
Let's go ahead and show some work here.
We'll have 4/3 times pi
times 27/2 cubed.
So, in parentheses, we'll have 27/2, close parenthesis.
And we'll cube this,
so we'll press the exponent key, or the caret,
three, Enter.
We want this as a fraction,
so we'll press Math, Enter, Enter.
So we have 19,683 divided by eight.
Now, again, for the exact volume,
we're going to leave pi in our answer.
So now we'll find the product of 4/3 and this fraction here.
So we'll have in parentheses
four divided by three
times 19,683
divided by eight,
close parenthesis, Enter.
Again, we don't want to have this as a decimal.
It's not good form to have a decimal times pi.
So we'll convert this back to a fraction
by pressing Math, Enter, Enter.
And we have 6,561 divided by two,
but we can't forget about the factor of pi.
So we have 6,561 divided by two pi.
And again, this is volume, so we'll have cubic centimeters.
Now let's also get our decimal approximation.
It is common to use 3.14 as an approximation for pi,
but we're going to use the pi key on the calculator
for more accuracy.
So, again, we have our fraction,
6,561 divided by two in parentheses,
and then times pi.
We press 2nd caret.
This brings up the pi.
Enter.
Now if we round this to two decimal places,
notice how the third decimal place is a four,
so we round down.
So this will be approximately 10,305.99 cubic centimeters.
So here we have the exact volume
and the volume rounded to two decimal places.
I do want to show that if we use 3.14 for pi,
it will change our decimal approximation.
The reason for this is that when we use the pi key,
we're using a much more accurate approximation
of pi than 3.14.
If we enter 6,561
divided by two
times 3.14,
notice how it would change our approximation
by over five cubic centimeters.
So this answer's going to be much more accurate.
So if you do have a pi key, you should use it.
I do want to mention one more quick thing.
If we're not sure about the units of our answer,
we can always leave the units in the formula
to determine the units.
Notice if we set this up as
the volume equals 4/3 times pi times r cubed,
if we wrote r as 27/2 centimeters cubed,
of course the product of 4/3 and 27/2 cubed
would still be this fraction here.
Then we have our factor of pi.
Notice how we can see why the units are cubic centimeters.
We have centimeters raised to the third power.
Finally, looking at the volume,
notice how this is telling us
that just less than 10,306 cubic centimeters
would fit inside our sphere.
I hope you found this helpful.