
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 22nd, 2017, 06:01 PM  #1 
Senior Member Joined: Jul 2016 From: USA Posts: 108 Thanks: 13  EASY Way to Find the Area of a Circle
I just thought of a quick simple way to find the area of a circle. Imagine a circle by which it's radius is expanding. At any point you can define the length of it's circumference by multiplying 2*radius*PI. Well then, 2PIr is simply the rate by which our circle is increasing in area with respect to the increasing radius. Integrate 2PIr PIr^2 I am quite sure many people have already thought of it though being as simple as it is. 
January 22nd, 2017, 10:43 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,661 Thanks: 427 
Here's a discussion of that observation. It works for spheres of arbitrary dimension. There are a number of interesting points of view and additional web references. calculus  Why is the derivative of a circle's area its perimeter (and similarly for spheres)?  Mathematics Stack Exchange Last edited by Maschke; January 22nd, 2017 at 10:48 PM. 
January 23rd, 2017, 01:37 PM  #3  
Senior Member Joined: Jul 2016 From: USA Posts: 108 Thanks: 13  Quote:
 
January 23rd, 2017, 01:55 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,080 Thanks: 723 
Don't start running in circles, Len !


Tags 
area, circle, easy, find 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find Area of a Quadrant of a Circle.  jayinwww  Algebra  2  November 25th, 2016 11:21 PM 
Need help with using horizontal slices to find the area of a quartercircle  leo255  Calculus  4  May 27th, 2014 01:41 AM 
Area enclosed by a semicircle and a quarter circle  yeoky  Algebra  4  May 3rd, 2014 02:06 AM 
find area of two circle  nabilkud  Algebra  1  October 20th, 2012 11:49 PM 
Find radius of circle if its area equals its circumferen  youtindia  Algebra  5  March 18th, 2011 10:36 AM 