A dog is leashed to point in the center of a large yard, so the area the dog is able to explore is circular. The leash is 18 feet long. What is the area of the region of dog able to explore? Round to the neartest tenth, show full working and explain

The region the dog is able to explore forms a circle, and the leash is essentially the radius of that circle. The formula for the area of a circle is given by

�

=

�

2

A=πr

2

, where

�

A is the area and

�

r is the radius.

In this case, the radius of the circle is the length of the leash, which is 18 feet. Now, we can plug this value into the formula:

�

=

�

×

(

18

feet

)

2

A=π×(18 feet)

2

Let's calculate this step by step:

�

=

�

×

324

feet

2

A=π×324feet

2

Now, to find the numerical value, we can use the approximation for

�

π to a few decimal places (let's use 3.14):

�

≈

3.14

×

324

feet

2

A≈3.14×324feet

2

�

≈

1015.76

feet

2

A≈1015.76feet

2

Now, rounding to the nearest tenth, the area of the region the dog is able to explore is approximately

1015.8

feet

2

1015.8feet

2

.

So, the dog can explore an area of approximately 1015.8 square feet.