A goat is tethered (tied up) to a stake in the ground with a 5 m rope. The goat can graze to the full length of the rope a full 360 around the stake. How much area does the goat have in which to graze?
well, what's the area of a circle of radius 5?
To find the area in which the goat can graze, we can use the formula for the area of a circle.
The formula for the area of a circle is: A = π * r^2, where A represents the area and r represents the radius.
Since the goat can graze in a full circle around the stake, the rope length represents the radius of the circle.
Given that the rope length is 5 m, the radius (r) is also 5 m.
Substituting the value of the radius into the formula, we get:
A = π * (5 m)^2
Calculating:
A = π * 25 m^2
A ≈ 78.54 m^2
Therefore, the goat has approximately 78.54 square meters of area in which to graze.
To find the area in which the goat can graze, we need to calculate the area of a circle with a radius of 5 meters. The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
In this case, the radius is 5 meters, so we can calculate the area as follows:
A = π(5^2)
To calculate this, we need the value of π, which is approximately 3.14159. Plugging in this value, we can find the area:
A ≈ 3.14159 * (5^2)
≈ 3.14159 * 25
≈ 78.54
Therefore, the goat has approximately 78.54 square meters of area in which to graze.