You are Here: Home >< Maths

# The area of a circle watch

1. why does the area of a circle = pi * r^2
2. (Original post by GayBoy)
why does the area of a circle = pi * r^2
using calculus, or not?
This page explains the non-calculus way i think, although it's not a totally acurate method, it's accepted as being a reasonable demonstration of how the area equation works.
3. A formal proof can be done using integration.

However, you can think about it more informally...all the formula says is that the area of a circle is proportional to its radius*radius (or diameter*diameter)...since the circle is a symmetrical shape, this should be fairly obvious. A square's area is proportional to length*length as well.
4. (Original post by Louise_1988)
using calculus, or not?
go for it...i want any type of proof
5. (Original post by GayBoy)
go for it...i want any type of proof
posted above!! (i'm not a pro-maths dude, but my teached did explain this one to us. Somebody who knows more on the subject may be able to explain better!)
6. imagine you draw a tiny tiny tiny segment of a circle. It's effectively a triangle. A triangle's area is .5(base*height). Now the base is easy, that's just r. But the height? Well if we call the tiny angle dx and it is in radians, then the height of the tiny segment is effecitvely it's arclength, which =rdx. So The triangle area = 0.5r^2dx

Now we define there to be 2pi radians in a circle (because that allows us to do radius*angle = arclength), so if we integrate our tiny triangles between 0 and 2pi:

Int(0.5r^2) between = 2pi and 0 =

(since r is a constant) [0.5r^2x] between 2pi and 0 =

[0.5r^2 * 2pi] - [0.5r^2 * 0] = 2*0.5pi*r^2 = pi*r^2 as required

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: August 1, 2004
Today on TSR

### Life lessons uni will teach you

Questionable decision-making and constant surprises

### University open days

1. Loughborough University
Fri, 21 Sep '18
2. University of Cambridge
Fri, 21 Sep '18
3. Richmond, The American International University in London
Fri, 21 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams