a Geometric Problem!!

[Antza]

I have a perfectly circular lawn area, which has a radius of r. I also have a ram, which is tied to a rope. The another end of the rope is fastened to a pole in the periphery of the lawn (at distance of r of the lawn center point). Exactly what should the rope lenght be so that the ram could eat HALF of the lawn area?
Don't know the answer myself, yet. Just figuring it out and I'll tell ya soon.

 

[d0ofy]

I think it's:

sqrt(Area of the lawn/2*pi)

I just took the formula for the area, A=pi(r)^2, and took half of A and solved for r.

Is the problem as easy as I think it is?

 

[teckmaster]

what if you were to divide you radius by 2 so that he could only eat half the radius

 

[d0ofy]

You just can't divide the radius by two. There's more area on the outer half than the inner half.

 

[Mday]

yes it is.... as simple as it seems...

the area of the lawn is pi*rr... let's call that 2A. so 2A = pi*rr... A is the area you want the ram to eat. so A = pi * RR, where R is the radius of the rope.

so R = sqrt(A/pi), and A = pi*rr/2

so R = sqrt(rr/2)

 

[Modeps]

do your own homework.

 

[thEnEuRoMancER]

If I understand correctly, the ram is tied to a pole in the circumference of the circle with radius r, not in its center point. Then we can rephrase the question as: find the radius R of a circle with the center point on the circumference of another circle with radius r, so that the overlapping area of both circles is exactly pi*r^2. This is not so simple.

Edit: this is my 666th post