A juice can is in the shape of a cylinder. It has a height if 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth.
To find the longest straw that can fit inside the juice can diagonally, we can use the Pythagorean theorem.
The height of the cylinder is 122 mm, and the diameter is 52 mm. Since the diameter is double the radius of the cylinder, the radius is 52/2 = 26 mm.
To find the diagonal, we can imagine a right triangle with the height of the cylinder as one side, the radius as another side, and the diagonal as the hypotenuse.
Using the Pythagorean theorem, we can find the length of the diagonal:
diagonal^2 = height^2 + radius^2
diagonal^2 = 122^2 + 26^2
diagonal^2 = 14884 + 676
diagonal^2 = 15560
Taking the square root of both sides:
diagonal = sqrt(15560) ≈ 124.8
So, the longest straw that can fit completely inside the juice can diagonally is approximately 124.8 mm. Rounding to the nearest tenth, the answer is 124.8 mm. Answer: \boxed{124.8}.