does anyone know how to work out the area of a circle..someone showed me a formula but it looked liked it was in a different language
xerus Tue 05/08/08 11:36
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The area of a circle is 3.142 x the diameter of the circle (the width across it from edge to edge, going through the centre).
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Bongle, you have just confused the issue by giving the formula for the CIRCUMFERENCE of the circle.
The AREA of a circle is given by squaring the radius and multiplying by 3.14
3.14 is an approximation for the value of Pi
Substitute more accurate values for greater precision.
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Oops, sorry, gen2 is right. I was trying to simplify the formulaic language and confused myself. Area of circle is 2 x pi x radius, circumference is pi x diameter.
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Bongle, you are STILL confused.
2 x pi x radius is the CIRCUMFERENCE
pi x diameter is the CIRCUMFERENCE
The AREA is pi x radius x radius
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gen2, again, you're right. Bad brain day. Sorry. However, we agree about the zeros in pi. Perhaps I'll leave formulas to you in future, although I can still remember -b plus or minus the square root of b squared minus 4 x a x c, all over 2 x a, to solve quadratics that won't factorise!! AND I could use it correctly.
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It's simple calculus.
OK, so you draw a circle. And another one. And another one.
You observe that the larger the circle's diameter (or radius), the larger the circumference.
So, circumference is proportional to diameter.
To turn this an equals sign (from a proportionality), you must add a constant. This is called a constant of propertionality.
C = x d.
So, x is this constant, so that we can write the equation with an equals sign. Usually this is written as Pi, ~= 3.14. You should be familiar with it by now :)
It's more useful to use the radius, so write C = 2 Pi r.
Now, to find the area of a circle.
Imagine the circle of being made up of consecutive circles -- one little one right in the centre, and more and more moving outwards, until the final one at the edge, which has a length that we call the circumpherence of this total circle.
The area is then just the circumpherence of all these circles, added up.
Area = 2 Pi x [r_1 + r_2 + r_3 + ...]
However, this assumes discreet circles (i.e., they have a thickness). But we know that they don't have a thickness. So you must add these circles together, knowing that they have infinitely thin width. To do this kind of thing (adding up over a continuum, instead of just discrete data), integration was invented.
So we integrate the circumferece, from 0 (at the centre of the circle) to r (the radius of the circle).
Area = integral from 0 to r of [2 Pi r] = Pi r^2
Hence, the area of a circle is 2 Pi r^2.
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Slip of the fingers/brain there in your last line fo3nix I'm afraid.
An extra 2 has crept in again
Hence, the area of a circle is 2 Pi r^2.
should read
Hence, the area of a circle is Pi r^2.
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Thanks, fo3nix, I now understand what integration means. Wish you'd been my teacher.
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gen2: you're right of course. The previous line contains the correct answer also.
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Perhaps also worth noting is that it's easy to proceed in this fasion and calculate the surface area of an ideal sphere. The volume of a solid sphere can then be calculated just as quickly.
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π r ² (as if you didn't already know)
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Divide a circle into an even number of equal sectors and then separate into two semicircles. Mesh the semicircles together using the sectors alternately as teeth and you create a figure roughly approaching a parallelogram in shape. The more sectors used, the closer is the resemblance.The length of the figure is half the circumference of the circle i.e.pi by r. The vertical height of the figure equals the radius of the circle. So the area of the parallelogram equals the area of the circle.Length by vertical height =pi by r by r = pi x r squared.
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