Bruiser's 10-foot long leash is tethered to the corner of his expansive 7 by 5 foot dog mansion. How much outdoor territory can he mark? (Use the approximation pi=3.14)
To find out how much outdoor territory Bruiser can mark, we need to calculate the area of the circle he can reach based on the length of his leash.
The length of the leash is given as 10 feet. Since the leash is attached to the corner of the dog mansion, it creates a circle with a radius of 10 feet.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Plugging in the values, the area can be calculated as:
A = 3.14 * (10^2)
A = 3.14 * 100
A = 314 square feet
Therefore, Bruiser can mark approximately 314 square feet of outdoor territory.
To determine the outdoor territory that Bruiser can mark, we need to calculate the area of the circular path allowed by his 10-foot long leash.
To start, we consider the radius of the circle. Since the leash is 10 feet long and forms the circumference of the circle, we can use the formula for the circumference of a circle:
Circumference = 2 * π * radius
We can rearrange this formula to solve for the radius:
radius = Circumference / (2 * π)
Plugging in the given length of the leash, we have:
radius = 10 feet / (2 * 3.14)
radius ≈ 1.59 feet
Now that we have the radius, we can calculate the area of the circle:
Area = π * radius^2
Plugging in the approximation π = 3.14 and the radius we found earlier, we have:
Area ≈ 3.14 * (1.59 feet)^2
Area ≈ 7.92 square feet
Therefore, Bruiser can mark approximately 7.92 square feet of outdoor territory.