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# Area of a circle

Video transcript

A candy machine creates small chocolate wafers in the shape of circular discs. The Diameter of each wafer is 16 millimeters. Whats it the area of each candy? So, the candy they say is in the shape of circular disc and they tell us that the diameter is 16 millimeters. If I draw a line across the circle, that goes through the center. The length of the line all the way across the circle through the center is 16 millimeters. The Diameter here is 16 millimeters. And they want us to figure out the area of the surface of the candy. Essentially the area of this circle. When we think about area, we know that the area of the circle is pi times the radius of the circle square. They gave us the diameter, what is the radius? well, you might remember that the radius is half of the diameter. Distance from the center of the circle to the outside, to the boundary of the circle. So, it will be this distance over here, which is exactly half of the diameter. So, would be 8 millimeters. So, where we see the radius, we can put 8 millimeters.
So, the Area is going to be equal to pi times 8 millimeters squared, which would be 64 square millimeters. And, typically this is written as pi after 64. So, you might often see it as 64 pi millimeter squared. Now, this is the answer 64 pi millimeters squared. But sometimes it is not satisfying to leave it as 64 pi millimeter squared. You might well say, that what number it is close to. I want a decimal representation of this. And we could start to use the approximate values of pi. So, the most rough approximate value which is tensed to be used is saying that pi, a very rough approximation, is equal to 3.14. So, in that case we can that this will be equal to 64 times 3.14 millimeters squared. We can get a calculator to figure out what this will be in decimal form. So, we have 64 times 3.14, gives us 200.96 So, we can say that the area is approximately equal to 200.96 square millimeters. Now if we want to get a more accurate representation of this, pi just actually keeps going on and on forever, we could use the calculator's internal representation of pi. In which case, we will say 64 times, and than we have to look for the pi on the calculator, it's up here this yellow, so I'll use the 2nd function to get the pi there. Now, we are using the calculator's internal representation of pi which is going to be more precise than what I had in the last one. And you can 201.06 (to the nearest hundred) So, more precise is 201.06 square millimeters. So, this is closer to the actual answer, because the calculator's representation is more precise than this very rough approximation of what pi is.