Question

a dog is leashed to a point in the center of a large yard, so the area the dog is able to explore is circular. the leash is 20 feet long. what is the area of the region the dog is able to explore? enter your numeric answer with no label.

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Identify the radius

The length of the leash is the radius of the circular area the dog can explore. So, \(r = 20\) feet.

Step3: Substitute the value of \(r\) into the formula

Substitute \(r = 20\) into \(A=\pi r^{2}\). We get \(A=\pi\times(20)^{2}\).

Step4: Calculate the value

\((20)^{2}=400\), and if we take \(\pi = 3.14\), then \(A = 3.14\times400=1256\).

Answer:

1256