Area of Grass for Tied Goat: 40.4383m^2

In summary, the "Area of Grass" refers to the amount of land or space required for a tied goat to graze on. It is calculated by multiplying the length and width of the designated grazing area. 40.4383m^2 is considered a suitable space for a tied goat to graze on for a short period of time, but it is not recommended for a goat to solely rely on this area for its nutritional needs. The appropriate "Area of Grass" can vary depending on factors such as breed, size, and grazing time, but a general guideline is to provide at least 10-15 square meters per goat for short-term grazing.
  • #1
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Consider a pasture bordering on a straight river. At 2m from the river, a goat is tied to a pole with a 4m long rope. What is the area of grass that the goat can graze?

The answer i got is about 40.4383m^2

Am i correct?
 
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  • #2
Yep - your answer is correct.

You used [tex]2\int^4_{-2}\sqrt{16-x^2}dx[/tex]

(or polar equivalent),

right?
 
  • #3


Yes, your calculation of 40.4383m^2 for the area of grass that the goat can graze is correct. This is a simple application of geometry, where the area of a circle with a radius of 4m (representing the length of the rope) is calculated to be approximately 40.4383m^2. This means that the goat has access to a circular area of grass with a diameter of 8m, centered around the pole to which it is tied. This is a good estimate for the amount of grass that the goat can graze in this scenario.
 

1. What is the significance of the "Area of Grass" in the context of a tied goat?

The "Area of Grass" refers to the amount of land or space required for a goat to graze on when it is tied to a specific location. This measurement is important in ensuring that the goat has enough space to move around and access enough grass for its nutritional needs.

2. How was the "Area of Grass" for a tied goat calculated?

The "Area of Grass" for a tied goat was calculated by measuring the length and width of the designated grazing area and multiplying them together. In this case, the calculation was done using the dimensions of 40.4383m^2 provided in the question.

3. Is 40.4383m^2 enough space for a tied goat to graze on?

The answer to this question depends on several factors such as the breed and size of the goat, the quality and density of the grass, and the amount of time the goat will be tied up. However, in general, 40.4383m^2 is considered a suitable space for a tied goat to graze on for a short period of time.

4. Can a tied goat survive solely on grazing in a 40.4383m^2 area?

It is not recommended for a goat to solely rely on grazing in a 40.4383m^2 area for its nutritional needs. While this may provide enough space for the goat to move around and access some grass, it may not provide enough variety or quantity of grass to meet all of its nutritional requirements. Supplemental feed and a larger grazing area are recommended for a goat's overall health and well-being.

5. How can I determine the appropriate "Area of Grass" for a tied goat?

The appropriate "Area of Grass" for a tied goat can vary depending on the factors mentioned in question 3. A general rule of thumb is to provide at least 10-15 square meters per goat for short-term grazing. It is also important to regularly monitor the goat's behavior and physical condition to ensure that it is getting enough food and exercise in the designated grazing area.

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