Question

a goat is tethered to a rope that is 3.65 meters long. what is the maximum area of grass that the goat can graze on? a = 41.83265 m²

Explanation:

Step1: Recall the formula for the area of a circle

The area formula for a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle. In this case, the length of the rope is the radius of the circular area the goat can graze, so \(r = 3.65\) meters.

Step2: Substitute the value of \(r\) into the formula

Substitute \(r = 3.65\) into \(A=\pi r^{2}\). Using \(\pi\approx3.14159\), we have \(A = 3.14159\times(3.65)^{2}\).
First, calculate \((3.65)^{2}=3.65\times3.65 = 13.3225\).
Then, \(A=3.14159\times13.3225\).
\(A = 41.83265\) (rounded to five decimal places as in the given answer).

Answer:

\(41.83265\space m^{2}\)