Final answer:
The area of the field that a goat tied to an 8m rope can graze is calculated using the area formula of a circle, resulting in approximately 201.06 square meters.
Step-by-step explanation:
The question at hand involves calculating the area that a goat can graze if it is tied to an 8-meter rope on a field. This is a problem related to geometry and specifically involves calculating the area of a circle given its radius. Since the goat is tied to an 8m rope, it can move in a circle around the point it is tied to, making the length of the rope the radius of the circle of grass that the goat can graze.
To calculate the area that the goat can graze, we use the formula for the area of a circle, which is A = πr^2, where 'A' is the area, 'π' is the constant pi (approximately 3.14159), and 'r' is the radius. Substituting the given radius of 8 meters, we calculate the area as follows:
A = π(8m)^2
A = π(64m^2)
A = 3.14159 × 64m^2
A ≈ 201.06m^2
Therefore, the area of the field that the goat can graze is approximately 201.06 square meters.
The area that the goat can graze can be represented as a circle with the rope as the radius. Since the rope is 8m long, the radius of the circle is also 8m. Using the formula for the area of a circle, which is A = πr², we can calculate the area. Plugging in the value of the radius (8m) into the formula, we get A = π(8m)². Simplifying this equation, we get A = π(64m²), which is approximately 201.06m².