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### Course: MAP Recommended Practice>Unit 8

Lesson 1: Area and circumference of circles

# Relating circumference and area

Sal uses formulas and a specific example to see how area and circumference relate..

## Want to join the conversation?

• At Sal mentions that from Circumference you can figure out Radius; and then from Radius you can figure out Area. What does he mean by that?
• If you know the circumference (say 20pi), you can find the radius, because every circumference is just the radius times 2 times pi. We can work backwards and divide 20 pi by pi, to get 20, then divide that by 2 to get the radius of 10. You can find any area if you have the radius, because all areas of circles are pi times the radius squared. If our radius is 10, then 10x10 is 100, and times that by pi to get the area of 100 pi (or about 314 units squared)
• Wait, where did 2 pi r come from?I just don't understand pretty much anything in this video.I need help!
• 2 pi r is the way to find the circumference when you have the radius.
• I am really, really confused. Where does the 2*pi*r come from? Can someone explain to me how this works??
• Pi is the ratio of circumference over diameter. 2 and r come from the formula of diameter.
You have to find circumference of a circle. Pi comes here because of its ratio. 2 and r comes because it equals the diameter.
So pi times 2 times r is basically circumference over diameter times diameter which gives circumference.
So that is where 2*pi*r comes from.
Hope this helps.
• how do i find the diameter of a circle when all i have is circumference
• If you measure a number of different circle circumferences and compare them to their diameters you will always find that there is a constant relationship between the two elements [C - circumference and d-diameter] which we call π. This can be expressed as C/d = π. C & d are in a constant proportion to each other (if you increase d then C will also increase (that constant proportion is π). If you know two of the values in this equation then with some algebraic manipulation you can rearrange the formula to give you the answer you require. If you have C and want to find d; then multiply out d whilst dividing by π to get C/π = d.
• 😭 why is this so hard
• The majority of this segment is just for you to remember the circumference and area formula for circles, once you remember that and you apply them to your equations it'll become much easier.
• Could someone please explain the whole 'pi * pi squared' part at ? I'm not quite getting it. Does it influence the outcome because the pi squared is in the denominator, or not? I'm pretty sure I've already learned the answer to my question, but I'm having a momentary lapse of memory on the subject. :/ Thanks.
• Usually Sal goes through all the steps but in this case he took a few shortcuts. Here's how I figured it.
A = PI r^2
A = PI(C/2PI)^2 <- put the formula for radius into the formula for area.
A = PI(C^2/2^2 PI^2) <- note that both 2 and PI are squared in this step
A = PI(C^2/4PI^2)
A = PI(C^2)/4PI^2
A = C^2/4PI <- at this step it seems like some kind of magic happened to get rid of the squared PI in the denominator but think of it like this:

It's basically PI/PI^2. What if we used regular numbers instead of PI? Something like ...
4/4^2. So now that's 4/16 which reduces to 1/4. The exponent has vanished! Basically multiplying any number by its reciprocal cancels that number out to make 1 and if there's an exponent it will reduce the exponent by 1. Yeah, I bet someone could explain this better than I did. :)
• At , how is 2 pi squared equal to 4 pi squared?
Also, how is pi divided by pi squared 1 over pi? Why doesn't he include the 4?
• youre making me more confused than i already am
• If anyone is in seventh grade, we all know that we have half a mind for this stuff. No comprendo, nino.
• what is the circumference of a circle and area of a circle?