Can anyone prove to me why the area of a circle is pie multiplied by the radius squared, why does it work? how

Question

what i want to know is why does it work, is there a proof you could use to show that it would work etc

Answer 1

Wikipedia to the rescue.

http://en.wikipedia.org/wiki/Area_of_a_circle

There are some pretty cool explanations here.

Answer 2

You can prove it using integral calculus.

The formula for a circle is x^2 + y^2 = r^2. If you graph this you will have a circle with the center at (0,0) with a radius of r.
Since you can only integrate functions, and a circle is not a function, you have to integrate a semicircle. (Either the portion above the x-axis, or the portion below.)

If you section a semicircle into rectangles with one side going from the x-axis vertically to a point on the semicircle and take the sum of the area of the rectangles, it approximates the area of the semicircle. The smaller the width of the rectangles you section, the closer to the area of the semicircle you get. The integral is the limit as the width of the sections approaches 0 (the smallest width section) of the sum of the rectangles, taken from x = -r to x = r. This limit works out to 1/2 * pi * r^2. The area of a full circle would be double that, or pi * r^2. Sorry I can't draw you a picture in a text box.

In other words, the area of a circle is the integral of the circumference. When you start doing calculus and analytic geometry, you will start to see how cool these relationships are.

Answer 3

The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius.A circle can be cut and rearranged to closely resemble a parallelogram of area pi times the square of the radius,By dividing the circle into more than eight slices, the approximation obtained in this manner would be even better. By dividing the circle into more and more slices, the approximating parallelograms approximate the area of the circle arbitrarily close. This give a geometric justification that the area of a circle really is "pi r squared".

Answer 4

you can try to approximate the circle with triangles ( for instance )
first with 4 triangles and then addup the area of the triangles.
next with 8 triangles and then addup the area of the triangles.

etc, in the limiting case you will get a that the area of the circle is a constant multiplied by the radius squared. the constant happens to be pi.

Answer 5

Archimedes proved that the area inside a circle is equal to the area of a right triangle whose legs are the length of the circle circumference and the length of the circle's radius. The Circumference of a circle is 2πr and the radius is r so the area of the circle is 1/2(r*2πr). The result is π(r^2)

Answer 6

The formula for the area of a circle is pi times r2 (r x r), so divide the area by pi then find the square root of that answer.

Answer 7

FYI, it is just "Pi" not "Pie."

Pi is just the ratio of the circumference of a circle to its diameter.

C = pi * diameter
C/diameter = pi * diameter / diameter
pi = Circumference / Diameter

It's just a mysterious number that is always true. Similar to the number e.

Answer 8

The circumference of a circle is 2*pi*r
If you integrate the circumference you will get the area of the circle. r is your variable

When you integrate you get pi*r^2

Answer 9

ask Egyptians mate

Answer 10

is this your maths homework ? :)
sorry I can't remember, i think i used to know
here's a website
http://www.mathreference.com/geo,circle.html