Question
a goat is tied by a rope 5\2 m long to a peg I some grass the goat eats one metre square of grass in 28min how long does it take to eat all that it can reach
Answers
GPT-4o mini
To determine how long it takes for the goat to eat all the grass it can reach, we need to calculate the area that the goat can graze given the length of the rope and then find out how long it takes to eat that area.
1. **Calculate the grazing area**:
The goat is tied with a rope that is \( \frac{5}{2} \) meters long, which is 2.5 meters. The area accessible to the goat is a circle with a radius of 2.5 meters. The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius.
Substituting \( r = 2.5 \):
\[
A = \pi (2.5)^2 = \pi (6.25) \approx 19.63 \text{ square meters}
\]
2. **Calculate the time to eat this area**:
The goat eats 1 square meter of grass in 28 minutes. Therefore, to find out how long it takes to eat \( 19.63 \) square meters, we multiply the area by the time per square meter:
\[
\text{Total time} = 19.63 \text{ m}^2 \times 28 \text{ min/m}^2
\]
\[
\text{Total time} \approx 549.64 \text{ minutes}
\]
Thus, it will take the goat approximately **550 minutes** to eat all the grass it can reach.
1. **Calculate the grazing area**:
The goat is tied with a rope that is \( \frac{5}{2} \) meters long, which is 2.5 meters. The area accessible to the goat is a circle with a radius of 2.5 meters. The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius.
Substituting \( r = 2.5 \):
\[
A = \pi (2.5)^2 = \pi (6.25) \approx 19.63 \text{ square meters}
\]
2. **Calculate the time to eat this area**:
The goat eats 1 square meter of grass in 28 minutes. Therefore, to find out how long it takes to eat \( 19.63 \) square meters, we multiply the area by the time per square meter:
\[
\text{Total time} = 19.63 \text{ m}^2 \times 28 \text{ min/m}^2
\]
\[
\text{Total time} \approx 549.64 \text{ minutes}
\]
Thus, it will take the goat approximately **550 minutes** to eat all the grass it can reach.