- [Teacher] A candy machine creates small chocolate wafers
in the shape of circular discs.
The diameter, the diameter of each wafer is 16 millimeters.
What is the area of each candy?
So, the candy, they say it's the shape of circular discs.
And they tell us that the diameter
of each wafer is 16 millimeters.
So if I draw a line across the circle
that goes through the center, the length of that line
all the way across the circle
through the center is 16 millimeters.
So let me write that, so diameter, the diameter
here is 16 millimeters and they want us to figure out
the area, the area of the surface of this candy.
Or essentially the area of this circle.
And so when we think about area,
we know that the area of a circle, the area of a circle
is equal to pi times the radius of the circle squared.
Times the radius of the circle squared,
and you say, well they gave us the diameter,
what is the radius?
Well, you might remember the radius
is half of diameter, so distance from the center
of the circle to the outside, to the boundary of the circle.
So it would be this distance right over here,
which is exactly half of the diameter.
So, it would be eight millimeters.
So, where we see the radius, we could put eight millimeters.
So the area is going to be equal
to pi times eight millimeters squared,
which would be 64, 64 square, 64 square millimeters.
And typically, this is written with pi after the 64,
so you might often see it as this is equal
to 64 pi, 64 pi millimeters squared,
millimeters squared, millimeters squared.
Now, this is the answer, 64 pi millimeters squared,
but sometimes it's not so satisfying
to just leave this pi, you might say,
"Well, I wanna get a estimate of what number
"this is close to, I wanna decimal representation of this."
And so we can start to use approximate values of pi.
So, the most rough approximate value that tends
to be used is saying that pi,
a very rough approximation is equal to 3.14.
So in that case, we could say that this is going
to be equal to 64, 64 times 3.14 millimeters,
millimeters squared and we can get our calculator
to figure out what this will be in decimal form.
So we have 64 times 3.14 gives us 200.96.
So we could say that the area is approximately equal to,
approximately equal to 200.96 square millimeters.
Now, if we wanna get a more accurate representation
of this, pi actually just keeps going on
and on and on forever, we could use the calculator's
internal representation of pi.
In which case we'll say 64 times
and then we have to look for the pi in the calculator,
it's up here in this yellow so I'll do
this little second function, get the pi there,
every calculator will be a little different.
But 64 times pi, now we're going to use
the calculator's internal approximation of pi,
which is going to be more precise than what
I had in the last one and you get
201, so let me put it over here so I can write it down,
so a more precise is 201, and I'll round, I'll round
to the nearest, I'll round to the nearest hundredth
so you get 201.06, so 201, so more precise
is 201.06 square millimeters.
So this is closer to the actual answer
'cause a calculator's representation is more precise
than this very rough approximation of what pi is.