Parametric Equations Problem

• May 7th 2007, 06:59 PM
machi4velli
Parametric Equations Problem
I am a bit confused about how to set up this problem:

A cow is tied to a silo with radius 6 by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. The rope must be 6pi in length, but I am not sure what to do with it from there.

I need to know how to solve this via parametric equations. Any help would be appreciated. Thanks.
• May 7th 2007, 08:59 PM
CaptainBlack
Quote:

Originally Posted by machi4velli
I am a bit confused about how to set up this problem:

A cow is tied to a silo with radius 6 by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. The rope must be 6pi in length, but I am not sure what to do with it from there.

I need to know how to solve this via parametric equations. Any help would be appreciated. Thanks.

Draw a picture. The required area is the area inside the larger circle (radius
6 pi) and outside the smaller (radius 6).

A = pi (6 pi)^2 - pi 6^2 = 36 pi (pi^2 -1).

RonL
• May 7th 2007, 11:21 PM
machi4velli
The rope is attached to a point on the outside of the silo (sorry, I didn't explain it well), so the outline of the shape formed by the outstretched rope does not form a circle. It makes a semicircle on one side but on the other the rope wraps around the silo and returns to a point on the opposite side of the silo, it looks similar to the graph of the polar equation r = 1 + cos(theta)