Topic C: Use equations and inequalities to solve geometry problems
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A candy machine creates small chocolate wafers in the shape of circular discs. 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. 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 the diameter here is 16 millimeters. And they want us to figure out 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 is equal to pi 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 1/2 of the diameter. It's the 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 1/2 of the diameter, so it would be 8 millimeters. So where we see the radius, we could 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 with pi after the 64. So you might often see it as this is equal to 64 pi millimeters squared. Now this is the answer, 64 pi millimeters squared. But sometimes, it's not so satisfying to just leave it as pi. You might say, well, I want to get a estimate of what number this is close to. I want a decimal representation of this. And so, we could 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 times 3.14 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 200.96 square millimeters. Now if we want to 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. And 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 more precise is 201. And I'll round to the nearest hundreds, so you get 201.06. So more precise is 201.06 square millimeters. So this is closer to the actual answer, because a calculator's representation is more precise than this very rough approximation of what pi is.