To find the longest straw that can fit diagonally inside a cylindrical juice can, we can visualize it as the diagonal of a right triangle where the height of the cylinder serves as one leg of the triangle, and the diameter of the base provides a base leg when considering the diameter.
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Identify the dimensions of the cylinder:
- Height (h) = 122 mm
- Diameter = 52 mm
- Radius (r) = Diameter/2 = 52 mm / 2 = 26 mm
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Find the diagonal (d) using the Pythagorean theorem: The diagonal of the cylinder will be the hypotenuse of the triangle formed by:
- The height (h = 122 mm)
- The diameter as its base (d = 52 mm)
However, for the diagonal, we need to calculate it across the circle formed by the cylinder's base: \[ \text{Diagonal} = \sqrt{h^2 + d^2} \] Here, \(d\) will be the diameter, and it is equivalent to the diagonal between two opposite points on the circle's edge: \[ d_{\text{circle}} = 2r = 52 \text{ mm} \]
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Compute the diagonal length: \[ \text{Diagonal} = \sqrt{(122)^2 + (52)^2} \] \[ = \sqrt{14884 + 2704} \] \[ = \sqrt{17588} \] \[ \approx 132.6 \text{ mm} \]
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Round to the nearest tenth: The longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.
Thus, the answer is 132.6 mm.