A rectangular box is 6 in. wide, 6 in. tall, and 12 in. long. What is the diameter of the smallest circular opening through which the box will fit?
hypotenuse diagonal of square
6^2 + 6^2 = d^2
d = 6 sqrt 2
To find the diameter of the smallest circular opening through which the box will fit, we need to determine the diagonal of the box. The diagonal can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length (L), width (W), and height (H) of the box form a right-angled triangle. The diagonal (D) is the hypotenuse, and the sides are the length and width.
Using the Pythagorean theorem, we can calculate the diagonal:
D = √(L^2 + W^2)
D = √(12^2 + 6^2)
D = √(144 + 36)
D = √180
D ≈ 13.42 inches
Therefore, the diameter of the smallest circular opening through which the box will fit is approximately 13.42 inches.