The Pythagorean Theorem in Three Dimensions Practice
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Question
A juice can is in the shape of a 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. (1 point)
mm
To find the length of the longest straw that can fit completely inside the juice can diagonally, we need to find the diagonal of the cylinder.
The diagonal can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can treat the height and the diameter of the can as the two legs of a right triangle, with the diagonal as the hypotenuse.
Using the formula for the diagonal of a cylinder:
diagonal = √(height^2 + diameter^2)
Substituting the given values:
diagonal = √(122^2 + 52^2)
diagonal = √(14884 + 2704)
diagonal = √17588
diagonal ≈ 132.6 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.