Home > maths, Uncategorized > Area And Circumference of a Circle : pi

## Area And Circumference of a Circle : pi

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This is a basic guide to using pi to find the area and circumference of a circle using pi. And also explores why pi makes our formulae work.

area =πr2

circumference = 2πr or πd

where r = radius and d=diameter

Area

First lets look at the area of a circle, given by area =πr2. This is simple enough to use, we multiply the radius by itself and then by pi.
Does this make sense?
Well r squared is at least going to be an area but it might be a bit small so we multipy by pi. However this doesn’t explain much until we consider what pi is, the easiest way i find to do this is as follows
If we imagine a square that the circle fits inside perfectly(so it touches all four sides like the one above) r squared would give us one quadrant, so the area of that square is 4 x r2 . Of course the circle’s area is a bit smaller so we need to find the ratio between the areas of the square and circle. If we then times this value by four we have a magic constant to multiply r squared by to find the area of a circle (we times by four because we need the area of 4 quadrants and r squared gives us one).
Now this magic constant is pi (which makes sense being just over 3, meaning the area of the circle is just over 3/4 of the area of the square).
Circumference
The circumference of a circle is given by 2πr or πd. This seems simple, we just multiply the diameter (2r) by our magic constant pi.
Does this also make sense?
seeing as we only have one r this time so only one length it seems we are just finding a factor to increase the length by to make a different length(the circumference) which makes sense.
Again lets consider the square into which our circle fits perfectly, the perimeter of this square would be 4 time the length of one of the sides.
Now the length of the sides = the diameter so the perimeter is 4d.
Notice again that the value we are trying to find for the square is multiplied by 4, but for a circle were going to need a ratio that is a bit smaller.
So we need to replace the 4, for a square, with another, smaller, number — it seems pi will do the job.
Conclusion
To me when I consider pi I don’t look at it as a magical fundamental constant, but more a magical fundamental constant multiplied by four, because when I consider how these formula work using pi this is how they seem to work.
So this new constant is really the ratio of
area of square to area of circle
perimeter of square to circumference of circle.
and it = pi/4 = 0.785398….
so if you have a value for a square and you want a similar value for the circle you just need to multiply it by this number and you’ll have your answer 🙂
thanks

By David Woodford

Categories: maths, Uncategorized
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• September 2, 2009 at 7:08 pm

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• October 23, 2009 at 2:26 am

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2. April 20, 2008 at 6:49 pm

Thanks for help 😀

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• September 2, 2009 at 7:09 pm

lol i know right

3. May 16, 2008 at 5:45 pm

how do you find the circomfrance of a cirlcle, when they give you the area???

4. May 17, 2008 at 10:52 am

the area is pi x r square
and the circumference is 2 x pi x r
so we can find are from square root of the area divided by pi
and times this by 2 pi to find the circumference

5. June 5, 2008 at 6:00 am

Thank you, its really helped me with my maths homweork.

6. July 2, 2008 at 4:06 pm

thanx 4 helpin meh

7. August 4, 2008 at 11:55 am

How do i find the diameter when i am given the area?

8. August 6, 2008 at 5:23 pm

re arrange a=pi x rsqaured and u get
r=sqaureroot of area/pi
then double it to find the diameter

9. October 30, 2008 at 10:02 pm

how you get area of a cirlcle from the circumfrence

10. November 1, 2008 at 12:18 pm

circumference is 2x pi x r and area is pi x r x r
so, area = pi x square(circumference/2 x pi)
area = circumference squared / 4 pi

hope that helps

11. November 5, 2008 at 1:37 pm

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12. November 5, 2008 at 2:37 pm

area = circumference squared / 4 pi

that part

13. November 19, 2008 at 8:55 pm

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14. November 19, 2008 at 8:56 pm

that was great

15. December 21, 2008 at 3:59 pm

why pi, but not 22/7

16. December 22, 2008 at 12:27 pm

22/7? wasn’t that just an approximation of pi used before they invented calculators.

17. January 13, 2009 at 12:07 am

this is to much work

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22. February 4, 2009 at 1:45 am

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23. February 20, 2009 at 11:52 pm

how do you find the area of 3/4 of a circle?
also how do you find the area of 1/4 of a circle?

24. February 21, 2009 at 11:32 am

just multiply the area of the whole circle by 3/4 or 1/4. For any part of a circle where you know the angle at the middle you can multiply the area of the whole circle by that angle divided by 360 (or 2pi if your using radians)

25. February 22, 2009 at 7:11 am

why is the pi of 500 decimal number different from that of 10 or maybe 100

• February 22, 2009 at 5:08 pm

what do you mean by the “pi of 500”?

26. March 15, 2009 at 2:08 am

hey um if there is a circle inside a square and the radius is 14 but the square has no measurement how do i find the anwser (all angles are right angles)

27. March 15, 2009 at 11:25 am

well the radius of the circle will be 1/2 the length of on of the sides so each side will be of length 28

assuming the circle touches all four sides of the sqaure

28. March 24, 2009 at 8:42 pm

why in the world we use Pi to calculate area of a circle?

• March 25, 2009 at 11:53 am

if you have a method not involving pi please tell me

29. March 24, 2009 at 9:58 pm

how do u find the area of the diameter.

30. March 24, 2009 at 9:58 pm

xD

31. March 24, 2009 at 10:00 pm

thank you so much it really help me thank you again =D know i can do my homework better than i did before.

32. March 24, 2009 at 10:14 pm

i really love math but i didnt get that part

33. March 24, 2009 at 11:00 pm

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• May 13, 2009 at 7:44 pm

this makes a lot of sence to me im learning it at school cause i want to be a teacher!!!!!

• May 14, 2009 at 5:43 pm

Glad I could be of help,

David (Author)

34. April 4, 2009 at 11:00 pm

THANKS

35. April 10, 2009 at 1:31 am

Hi All,

Would you know the latest new exact formula for calculating Pi Number? If so please visit to this link:

At the link I’ve been posting general exact formula for Pi Number in form of the sum two arcsin. Maybe useful for you.Thx.

Best Regards,
Rohedi.

36. April 16, 2009 at 11:19 pm

Well @Trevorpythag,

there are the post of exact value of Pi number in Golden Ratio expression.

Best Regards,
Rohedi.

• April 23, 2009 at 3:09 pm

David

37. May 13, 2009 at 4:48 pm

wow! I just learned allot!

38. May 18, 2009 at 12:00 pm

good yarr

39. May 18, 2009 at 12:00 pm

good yarr

40. June 3, 2009 at 9:07 pm

i didn’t know how to do a circumference and area of a circle but now im a wiz sooo yo homiez check this cooolo website it helps you it helped me

• June 4, 2009 at 10:07 am

Thankyou,
David

41. June 27, 2009 at 9:16 am

very interesting but bifficult

42. July 1, 2009 at 4:01 pm

yoyoyo true that

43. August 21, 2009 at 12:03 pm

Hello Trevor Iwas trying to figure sqft of 8 ft radious Ifallowed the methed to the best of my knowledge which was 8 x 8= 64 x0.785398= 50.26 sqft please reply if this is correct thank you Ali chahine

• August 21, 2009 at 2:56 pm

correction to my comment

If a circle has a radius of 8ft you can either do
A = pi x 8 x 8
or
find the diameter , d = 2 x 8 = 16 and then use the method above to get
A = 16 x 16 x 0.785398 = 201.061888…

david (trevor)

44. September 4, 2009 at 1:35 am

why does the area of a circle formula work

• September 4, 2009 at 9:43 am

IF you consider the square that touches all four sides of the circle as in the diagram in the post then r^2 gives the area of one quadrant. To find the area of the whole square we would multiply by 4 but the area of the circle is a fraction of the area of the sqaure (pi/4) so we must multiply by a smaller value than 4 which has been calculated to be pi

david

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46. September 15, 2009 at 11:05 pm

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• September 16, 2009 at 9:06 am