All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Around the ring (Posted on 2010-12-20)
Take the line segment whose endpoints are the points (1,0) and (-1,0) and a point of rotation (x,y).

If the segment is rotated all the way around the point it will trace out an annulus.

Find simplified formula for the area of this annulus in terms of x and y.

Redo this problem for a rectangle with corners at (1,1), (-1,1), (-1,-1), and (1,-1).

 No Solution Yet Submitted by Jer Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): part 1 spoiler -- whoops | Comment 3 of 9 |
(In reply to re: part 1 spoiler -- whoops by Charlie)

Charlie,

Just a question: why aren't the values 4pix and -4pix?

Pi*((x+1)^2+y^2)-pi*((x-1)^2+y^2)=4pix

pi*((x-1)^2+y^2)-pi*((x+1)^2+y^2) =-4pix

i.e. abs (4pix) The point being that the annular area for the second part can then conveniently be stated as abs(4pix)+abs(4piy), for {x>1,x<-1;y>1,y<-1}

Edited on December 21, 2010, 2:11 pm
 Posted by broll on 2010-12-21 06:44:49

Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information