Fido the dog is on the end of a 6 foot chain. he chain is attached to the corner of his 3 foot by 4 foot doghouse. How much are can Fido cover outside of his house?
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To find out how much area Fido can cover outside of his doghouse, we need to determine the length of the chain and calculate the area it can cover.
First, let's use the Pythagorean theorem to find the length of the chain. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the chain forms the hypotenuse of a right triangle, with the sides of the doghouse forming the other two sides. The length of one side of the doghouse is 3 feet, and the length of the other side is 4 feet. Using the Pythagorean theorem:
Length of chain^2 = 3^2 + 4^2
Length of chain^2 = 9 + 16
Length of chain^2 = 25
Taking the square root of both sides, we find:
Length of chain = √25
Length of chain = 5 feet
Therefore, the length of the chain is 5 feet. This means that Fido can move up to a maximum distance of 5 feet from the doghouse.
Next, we need to calculate the area that Fido can cover outside of his doghouse. Since Fido can move in a circular shape around the doghouse, the covered area will be a circle.
The formula to calculate the area of a circle is:
Area = π * r^2
where π (pi) ≈ 3.14159 and r is the radius of the circle.
In this case, the radius of the circle is equal to the length of the chain, which is 5 feet. Using the formula:
Area = 3.14159 * 5^2
Area = 3.14159 * 25
Area ≈ 78.54 square feet
Therefore, Fido can cover approximately 78.54 square feet outside of his doghouse.