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 completely inside the juice can diagonally, we need to determine the length of the diagonal of the juice can.
First, let's calculate the length of the diagonal of the juice can's base. The diameter of the base is 52 mm, so the radius (r) is half of the diameter, which is 52/2 = 26 mm.
Using the Pythagorean theorem, we can find the length of the diagonal of the juice can's base (the hypotenuse of a right triangle formed by the radius and the height):
diagonal_base = √(r^2 + h^2)
diagonal_base = √(26^2 + 122^2)
diagonal_base ≈ √(676 + 14884)
diagonal_base ≈ √15560
diagonal_base ≈ 124.7 mm
Next, we need to calculate the height of the juice can plus the diagonal_base because the straw will be going from the top of the can to the bottom, diagonally:
height_with_diagonal_base = h + diagonal_base
height_with_diagonal_base = 122 + 124.7
height_with_diagonal_base ≈ 246.7 mm
Finally, the longest straw that can fit completely inside the juice can diagonally is equal to the height_with_diagonal_base:
longest_straw ≈ 246.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 246.7 mm.