To determine the longest straw that can fit completely inside the cylindrical juice can, we can use the relationship between the height and the diameter of the cylinder. The longest straw will extend from one corner of the base to the opposite corner of the top face, forming a diagonal.
We will use the Pythagorean theorem in three dimensions. The formula for the longest diagonal \(d\) inside a cylinder can be calculated as follows:
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Find the radius of the cylinder: \[ r = \frac{\text{diameter}}{2} = \frac{52 \text{ mm}}{2} = 26 \text{ mm} \]
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Use the formula for the diagonal: The formula for the diagonal \(d\) in a cylinder is: \[ d = \sqrt{(2r)^2 + h^2} \] where \(2r\) is the diameter of the base of the cylinder (across the width), and \(h\) is the height.
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Substitute the values into the formula:
- The diameter \(2r = 52 \text{ mm}\)
- The height \(h = 122 \text{ mm}\)
Therefore, we have: \[ d = \sqrt{(52)^2 + (122)^2} \] \[ d = \sqrt{2704 + 14884} \] \[ d = \sqrt{17588} \] \[ d \approx 132.6 \text{ mm} \]
After rounding to the nearest tenth, the length of the longest straw that can fit completely inside the juice can is approximately 132.6 mm.