Question

A dog is leashed to the corner of a house with a 20 ft long leash. How much running area does the dog have? Round your answer to the nearest square foot, if necessary.

The dog has about ___ square feet of running area.

Answer 1

The dog has about 1257 square feet of running area.

Step-by-step explanation:

To find the running area of the dog, we need to find the area of the circle with a radius of 20 ft.

The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.

Using this formula, we can calculate the area as follows:

A = π(20^2) = 400π ft²

Rounding to the nearest square foot, the dog has about 1257 ft² of running area.

Answer 2

The dog's running area is approximately 942 feet².

Step-by-step explanation:

The dog is leashed to a fixed point, the leash has a length of 20 ft, therefore he can rotate around that point at the maximum distance equal to the length of the leash. This pattern forms a circle, but there is an obstruction, which is the corner of the house. This obstruction takes an arc of the original circle, so the running area of the dog is the area of the whole circle minus the area of the arc formed by the corner of the house.

`\text{dog's area} = \text{circle's area} - \text{arc's area}\\\\\text{dog's area} = pi*(20^2) - (90)/(360)*pi*(20^2)\\\\\text{dog's area} = (270)/(360)*pi*(400)\\\\\text{dog's area} = 942.477\text{ feet}^2`

The dog's running area is approximately 942 feet².