## 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 =πr^{2}

circumference = 2πr or πd

where r = radius and d=diameter

**Area**

First lets look at the area of a circle, given by area =πr

^{2}. 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 r

^{2}. 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.

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 🙂

I welcome comments, improvements or errors in this post. Please leave your comments below or email me at david.woodford.4@googlemail.com

thanks

By David Woodford

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

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

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

thanx 4 helpin meh

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

re arrange a=pi x rsqaured and u get

r=sqaureroot of area/pi

then double it to find the diameter

how you get area of a cirlcle from the circumfrence

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

what is wit the gangsta on the top??? anyway where is the answer to wat Howell says said???

area = circumference squared / 4 pi

that part

that was shity

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why pi, but not 22/7

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

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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?

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)

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

what do you mean by the “pi of 500”?

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)

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

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

if you have a method not involving pi please tell me

how do u find the area of the diameter.

xD

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

i really love math but i didnt get that part

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Glad I could be of help,

David (Author)

THANKS

Hi All,

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

http://eqworld.ipmnet.ru/forum/viewtopic.php?f=3&t=148.

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.

Well @Trevorpythag,

Now, I give additional information that on the following link:

http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=157,

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

Best Regards,

Rohedi.

Thanks for the link 🙂

David

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Thankyou,

David

very interesting but bifficult

yoyoyo true that

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

correction to my commentIf 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)

why does the area of a circle formula work

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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