Maximizing Cow Grazing: Solving Area and Quadratic Equations with Tethered Cows

[Paradiselovek]

Area/Quadratic NEED HELP****

The problem is:

A cow is tethered by a piece of rope 50m long. The rope is fastened to a hook located 10 m from the corner of the longest side of a barn measuring 60m by 30 m. Over how much ground can the cow graze.

I add the information above to the diagramp below:

http://www.freeimagehosting.net/uploads/a875067c70.jpg

I try to find the area of the circle then divide it in half (since it half a circle) but I'm not sure so please help

 

[berkeman]

Start by drawing both the circle (R=50m) and the rectangle, with the center of the circle where you've shown the tether spot. Do you see a way that you could divide that up into regions, to get the various areas that make up the grazing area?

Hint -- I think there are at least 3 pieces that you will calculate the area of differently, and then sum them up for the total grazing area...

 

[Paradiselovek]

Start by drawing both the circle (R=50m) and the rectangle, with the center of the circle where you've shown the tether spot. Do you see a way that you could divide that up into regions, to get the various areas that make up the grazing area?

Hint -- I think there are at least 3 pieces that you will calculate the area of differently, and then sum them up for the total grazing area...

Okay, thank you. Are the 3 pieces in the tether spot include 1/4 of a circle (2 of them)with a radius of 10 m, then 1 (1/2) a circle?I'm wondering if that right, if not can you please give me a bit more hint. Thank you so much ^^

http://www.freeimagehosting.net/uploads/2e83ed54ea.jpg

 

[Astronuc]

The hook on the upper side of the barn is one pivot point for an semicircle of 50 m.

When the cow passes below the plane (line) of the upper side of the barn, the corner becomes a pivot point for a smaller circle, of a shorter radius.

Then the cow can pass by the bottom right corner, at a still smaller radius.

Think about what happens are each corner.

 

[Paradiselovek]

The hook on the upper side of the barn is one pivot point for an semicircle of 50 m.

When the cow passes below the plane (line) of the upper side of the barn, the corner becomes a pivot point for a smaller circle, of a shorter radius.

Then the cow can pass by the bottom right corner, at a still smaller radius.

Think about what happens are each corner.

Hi for the solution above, I draw out my circles, but I still don't know how to find the area of the side circle one. Plz help

http://www.freeimagehosting.net/uploads/c17d20dfb6.jpg

 

[Astronuc]

If one has a radius, then one can find the area.

On the top the cow sweeps through a semi-circle (half-circle). On the side, the cow would sweep through a quarter circle (from horizontal to vertical) before it turns passes the corner.