0

The problem goes like this :

There is a circular field of radius = $r$ m (say 7 m), and a cow is tied with a rope of $x$ m on the circle. If cow grazes all the grass which is in its range then the cow would have grazed half of the total grass on the field. (Grass is uniform all over the field). Find the length of the rope (i.e., $x$).

I tried various methods like completing the circle from the arc made by cow, taking half the area of the field and finding the radius of another circle etc. but was unable to find the answer. Actually, I've no idea right now how to proceed.

[Note]
This is not my HW but a question which was given by a teacher to my class.

Jean Marie
  • 88,997
Mayank M.
  • 709
  • Sorry @Doug M it is not the right equation: as I understand it (and it's the classical goat's problem), the post to which the rope is attached is not the circles's center but is on its border. . See a complete solution at the end of this document: (http://www.houstonact.org/Pete/UH_presentation_problems.doc) – Jean Marie Sep 09 '16 at 08:27
  • You are right, I must have been late and I answered in haste. I thought the classic goat problem involved a silo, – Doug M Sep 09 '16 at 16:36

1 Answers1

0

You have a circle (where the cow lives) in a circle (where the grass is). What you now have to calculate is the radius of the inner circle, such that its area is exactly the half of the area of the outer circle. Reminder: To calculate the area of a circle use the formula $A=\pi \cdot r^2$.

EDIT: My answer was considering the post is in the cirlce. Else you might have your answer here

Community
  • 1
ctst
  • 1,442