A candy machine createssmall chocolate wafers in the shape of circular discs. The diameter of eachwafer is 16 millimeters. What is the area of each candy? So the candy, they say it'sthe shape of circular discs. And they tell us that thediameter of each wafer is 16 millimeters. If I draw a lineacross the circle that goes through thecenter, the length of that line all the way acrossthe circle through the center is 16 millimeters. So let me write that. So the diameter hereis 16 millimeters. And they want us tofigure out the area of the surface of thiscandy, or essentially, the area of this circle. And so when wethink about area, we know that the areaof a circle is equal to pi times the radiusof the circle squared. And you say, well, theygave us the diameter. What is the radius? Well, you might remember theradius is 1/2 of the diameter. It's the distancefrom the center of the circle to the outside,to the boundary of the circle. So it would bethis distance right over here, which is exactly1/2 of the diameter, so it would be 8 millimeters. So where we see the radius,we could put 8 millimeters. So the area is goingto be equal to pi times 8 millimeterssquared, which would be 64 square millimeters. And typically, this iswritten with pi after the 64. So you might oftensee it as this is equal to 64 pimillimeters squared. Now this is the answer,64 pi millimeters squared.
You are watching: Find the area of a circle whose circumference is
But sometimes, it's not sosatisfying to just leave it as pi. You might say, well, I want toget a estimate of what number this is close to. I want a decimalrepresentation of this. And so, we could start touse approximate values of pi. So the most rough approximatevalue that tends to be used is saying that pi, avery rough approximation, is equal to 3.14. So in that case, wecould say that this is going to be equal to 64times 3.14 millimeters squared. And we can get ourcalculator to figure out what this will bein decimal form. So we have 64 times3.14, gives us 200.96. So we could say that thearea is approximately equal to 200.96square millimeters. Now if we want to get amore accurate representation of this– pi actuallyjust keeps going on and on and onforever– we could use the calculator'sinternal representation of pi, in which case,we'll say 64 times, and then we have to look forthe pi in the calculator. It's up here inthis yellow, so I'll do this little second function. Get the pi there. Every calculator willbe a little different. But 64 times pi. And now we're going touse the calculator's internal approximationof pi, which is going to be more precisethan what I had in the last one. And you get 201– solet me put it over here so I can write it down–so more precise is 201. And I'll round to the nearesthundreds, so you get 201.06. So more precise is 201.06square millimeters. So this is closer tothe actual answer, because a calculator'srepresentation is more precise than this veryrough approximation of what pi is.