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).

(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