A dog is tied to a leash that is hooked tot he outside corner of a barn that measures 12ft x 20ft. The length of the leash is 16ft. What is the maximum area in which the dog can wander?
To find the maximum area in which the dog can wander, we need to determine the shape and size of that area. Since the dog is tied to a leash, it can move in a circle around the attachment point.
The attachment point is the outside corner of the barn, so the dog can move in a circle with a radius equal to the length of the leash, which is 16ft.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Therefore, we can calculate the maximum area:
A = π * r^2
A = π * (16ft)^2
A = π * 256ft^2
Using the value of π, which is approximately 3.14, we can approximate the maximum area:
A ≈ 3.14 * 256ft^2
A ≈ 803.84ft^2
Therefore, the maximum area in which the dog can wander is approximately 803.84 square feet.
To find the maximum area in which the dog can wander, we need to find the shape that has the largest area within the given constraints. In this case, the leash forms a circular boundary around the dog.
First, we need to determine the center of the circle. Since the dog is tied to the outside corner of the barn, the center of the circle will be the center of the barn itself. The dimensions of the barn are 12ft x 20ft, so the center will be at a point equidistant from each corner. The center coordinates are (12ft/2, 20ft/2) = (6ft, 10ft).
Next, we need to determine the radius of the circle. The leash has a length of 16ft, so the radius of the circle will be 16ft.
Now we can calculate the area of the circle using the formula A = πr^2. Plugging in the radius, we get:
A = π(16ft)^2 ≈ 804.25 square feet
Therefore, the maximum area in which the dog can wander is approximately 804.25 square feet.