Who is asking: Student
I have a problem I can't get. The problem is:
A goat is tied to one corner of a square pen 20 ft. on a side.
- If the goat's tether is 10 ft. long, what percentage of the grass in the pen can the goat reach?
- What should the length of the tether be so that the goat can reach half of the grass?
I drew a diagram. The goat is tethered to a post at the corner labeled P.
The area of the pen is
200 x 200 = 400 sq ft.
The region where the goat can graze is one-quarter of a circle of radiu 10 ft. The area of a circle is pi r2 and hence the area of the region where the goat can graze is
1/4 pi 102 sq ft.
Thus the percentage of the grass in the pen that the goat can reach is
which is approximately 20%.
Now try the second part of the problem.
Go to Math Central