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A dog tethered to a round building 2009-09-28
From mido:
One dog was linked to the outer wall of a building round of 20 meters in diameter. If the length of chain linking the dog sufficient turnover of half the distance around the building, What area can guard dog?
Answered by Harley Weston.
A two goat problem 2009-04-27
From Michael:
if you have a goat tied to a pole at one corner of a square paddock with one length of a side being 24m. what length must the rope be for the goat tied up to graze half the paddock? and if another goat is placed on the opposite corner and same length what is the amount of area they share grazing ?
Answered by Stephen La Rocque and Penny Nom.
A goat in a square paddock 2009-02-10
From lachlan:
A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m.

a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %?

b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be?

Answered by Penny Nom.
Sheep, goats, and hogs 2009-01-23
From La:
A man buys sheep, goats, and hogs, to the number of 100, for 100 crowns; the sheep cost him 1/2 a crown a-piece; the goats cost him 1-1/3 crowns a-piece; and the hogs cost him 3-1/2 crowns a-piece. How many had he of each?
Answered by Robert Dawson.
A goat tied to a rectangular barn 2008-11-02
From Misty:
If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor). When the rope goes around the barn, what is the new radius and How much of a circle can it make without hitting the barn or overlapping area you've already found and What is that area?
Answered by Stephen La Rocque.
Another goat problem 2008-02-13
From jasmin:
A farmer staked his goat at the corner of the barn 30 m long and 25 m wide so that the goat could eat the grass near the corner of the barn. He found that if the rope by which the goat was tied was lengthened by 10 m, the goat could graze over four times as much as the area. How long was the original rope, if in neither case it was as much as 25 m long?
Answered by Stephen La Rocque.
A goat problem 2007-03-06
From Tish:
This question has a, b, c parts.

1. A square barn measures 14 meters on each side.A goat is tethered outside by a rope that is attached to one corner of the barn:
a. Suppose that the length of the rope is 8 meters. On how many square meters of land is the goat able to graze? What shape is formed?
b. Suppose that the rope is made twice as long as in part a. On how many square meters of land is the goat now able to graze?
c. Lastly, an addition to the barn wabuilt making it rectangular with dimensions 14 meters by 20 meters and extended the ength of the rope to 24 meters, on how many square meters of land is the goat now able to graze? meters

Answered by Penny Nom.
The area of a sector and a triangle 2006-06-23
From Howard:
I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord.
Answered by Stephen La Rocque and Penny Nom.
A goat is tied to the corner of a 50 ft square outbuilding 2005-12-24
From Danielle:
Topic: A goat is tied to the corner of a 50 ft square outbuilding with a 40 ft. rope.
a) What is the measure of the partial circumference created as the goat walks at the full length of the rope?

b) Since the goat is trimming the grass from part of the outbuilding, how much of the perimeter of the outbuilding will the building owner have to trim?

Answered by Penny Nom.
George and his goat herd 2003-05-27
From A student:

George the bulgarian goatherd drives his father's goats into a valley each morning and lets them browse there all day before driving them home in the evening.

he notices that each morning the goats immediately separate into groups and begin to feed the number and sizes of the initial groups vary some days there are nine and so days there are three or fewer. there can be groups of one or the whole group.

about every five minites one goat breaks away from each feeding group and these breakaway goats form into a new group.

George has noticed that by the afternoon, even though the goats continue their regrouping the sizes of the groups have stabilised, and there is always seven feeding groups.

How many goats are there in the herd? What are the sizes of the feeding groups once they have stabilised?

Answered by Penny Nom.
A goat in a square pen 2001-10-19
From Brad:
A goat is tied to one corner of a square pen 20 ft. on a side.
  1. If the goat's tether is 10 ft. long, what percentage of the grass in the pen can the goat reach?

  2. What should the length of the tether be so that the goat can reach half of the grass?

Answered by Penny Nom.
A goat problem 2000-03-10
From Nancy:
A farmer has a fenced-in, circular field with an area of about one acre. A goat in the field is tethered to one of the fence posts with a rope which gives the goat approximately one-half acre of grazing area. To the nearest foot, how long is the rope?
Answered by Chris Fisher.
Grazing area for a goat 2000-03-10
From Amy:
A goat is tied in the middle of a side of a square building whose sides are 2 yards long. The rope is 4 yards long. What is the grazing area for the goat?
Answered by Harley Weston.



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