A juice can is in the shape of cylinder. It has a height of 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 diagonal that can fit completely inside the juice can, we need to find the diagonal of a rectangle formed by the height and the diameter of the cylinder.
The diagonal of a rectangle can be found using the Pythagorean theorem. The equation is:
diagonal^2 = height^2 + diameter^2
Substituting the given values into the equation:
diagonal^2 = 122^2 + 52^2
diagonal^2 = 14884 + 2704
diagonal^2 = 17588
Taking the square root of both sides to solve for the diagonal:
diagonal ≈ √17588
diagonal ≈ 132.6 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm. Rounded to the nearest tenth, it is 132.6 mm.