What is the minimum diameter of a round stock necessary to make a square key 5 inches to each side?
the square key has diagonal 5√2
That would also be the diameter of the smallest circle enclosing the square.
To determine the minimum diameter of a round stock necessary to make a square key, you can follow these steps:
Step 1: Find the diagonal of the square key.
The diagonal of a square can be found using the Pythagorean theorem: diagonal^2 = side^2 + side^2. In this case, the side length is 5 inches. So, diagonal^2 = 5^2 + 5^2.
Step 2: Calculate the diagonal.
Using the equation from Step 1, diagonal^2 = 25 + 25 = 50. Taking the square root of both sides, we find that the diagonal is √50 inches.
Step 3: Determine the minimum diameter.
The minimum diameter of the round stock should be equivalent to the diagonal of the square key. Therefore, the minimum diameter of the round stock necessary to make a square key with sides of 5 inches would be √50 inches.
To determine the minimum diameter of a round stock necessary to make a square key of a specific size, you need to calculate the diagonal distance of the square.
The diagonal of a square can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the diagonal of the square is the hypotenuse of a right triangle, with the two sides being the length of each side of the square.
Let's calculate the diagonal distance using the given side length:
1. Square the side length: 5 inches * 5 inches = 25 square inches.
2. Multiply the squared side length by 2: 25 square inches * 2 = 50 square inches.
3. Take the square root of the result: √(50 square inches) ≈ 7.07 inches.
Therefore, the minimum diameter of the round stock necessary to make a square key with 5 inches on each side is approximately 7.07 inches.