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CCSS Math: 7.G.B.4

- [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.