a dog is tied to a leash that is hooked to the outside corner of a barn that measures 12 x 20 feet. the length of the leash is 16 feet. what is the maximum are in which the dog can wander?
Make sure you have a diagram for this.
I had the dog being able to run 3/4 of a circle with a radius of 16 ft.
At that point the leash would bend around the other point of the barn along the shorter side of 12ft giving another 1/4 circle of radius 4 feet.
total area = (3/4)π(16^2) + 1/4(π(4^2))
= 192π + 4π = 196π square feet
thank you.. this is what i thought. just double checking
To find the maximum area in which the dog can wander, we need to determine the shape of the area that the leash allows the dog to roam. Since the leash is tied to the outside corner of the barn, it forms a quarter circle.
The radius of the quarter circle is equal to the length of the leash, which is given as 16 feet. The formula to calculate the area of a quarter circle is:
Area = (π * r^2) / 4
Let's substitute the value of the radius into the formula:
Area = (π * 16^2) / 4
= (π * 256) / 4
= 64π
So, the maximum area in which the dog can wander is 64π square feet.