To determine the longest straw that can fit completely inside the cylindrical juice can, we need to calculate the length of the diagonal that stretches from one point on the bottom circle of the cylinder to the opposite point on the top circle. We will use the Pythagorean theorem in three dimensions.
Given:
- Height of the cylinder (h) = 122 mm
- Diameter of the cylinder (d) = 52 mm
- Radius of the cylinder (r) = d / 2 = 52 mm / 2 = 26 mm
Now, we need to find the length of the diagonal from one edge of the base to the opposite edge of the top. This forms a right triangle where:
- One leg (the height of the cylinder) = h = 122 mm
- The other leg (the diameter of the base) = d = 52 mm
Using the Pythagorean theorem, the length (L) of the diagonal is given by:
\[ L = \sqrt{(d)^2 + (h)^2} \]
Substituting in the values we have:
\[ L = \sqrt{(52)^2 + (122)^2} \]
Calculating the squares:
\[ 52^2 = 2704 \quad \text{and} \quad 122^2 = 14884 \]
Adding these values:
\[ L = \sqrt{2704 + 14884} = \sqrt{17588} \]
Now, calculating the square root:
\[ L \approx 132.6 , \text{mm} \]
Therefore, rounding to the nearest tenth, the longest straw that can fit completely inside the juice can diagonally is approximately:
\[ \boxed{132.6} , \text{mm} \]
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