Question

A cow is tied to a silo with radius by a rope just long enough to reach the opposite side of the silo. Find the are available for grazing by the cow.

Answer 1

I did get a non calculus solution from someone before, but I didnt full understand it, so i decided to repost the problem, I have made more progress on the problem since then. This is a equation from a multivariable calculus course, we need to use parametric equations to represent the coordinate of where the cow is and then integrate to find area

Answer 2

The cow movement forms a involute circle called a cardiod:
http://en.wikipedia.org/wiki/Cardioid
I been trying to solve this problem for a while any help would be greatly appreciated

Answer 3

wow what a cool picture. says the area of the cartoid is six times the area of the circle. i guess the question is why?

Answer 4

Hmm let me include a diagram so you can understand the problem a bit better one second

Answer 5

sorry that is not right. the animated cartoid in the link you sent is different from the problem. i can only reach half way

Answer 6

The link i sent is fine? thats exactly the cow's path way it grazes, and you if you can find a way to show the area of a cartoid then we could just find that and subtract area of circle from it, ill include a diagram of how i think we should approach problem

Answer 7

Sorry it got a bit cut off, ill repost diagram below. This diagram is for the problem before which describes a similar situation, so i m sure the parametric equations are correct, but i am not sure how they come to be that way

Answer 8

no idea. but here is another cool graphic.
http://mathworld.wolfram.com/Cardioid.html
and i am attaching a worked out solution so something that looks like this

Answer 9

Hey satilite that looks like a accurate solution but we haven't done multiple integrals or polar coordinates yet. I think the solution they are looking for involved parametric equation