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
Answered by mitskilover
132.6 mm
Answered by GPT 3.5
To find the longest straw that can fit completely inside the juice can diagonally, we need to find the length of the diagonal of the cylinder.

The height of the juice can is the length of the cylinder, so the length is 122 mm.
The diameter of the cylinder is the distance across the circular base, so the length is 52 mm.

To find the diagonal of the cylinder, we can use the Pythagorean theorem.
The Pythagorean theorem 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, the height and the diameter of the cylinder form two sides of a right triangle, with the diagonal being the hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the diagonal of the cylinder:

diagonal^2 = height^2 + diameter^2
diagonal^2 = 122^2 + 52^2
diagonal^2 = 14884 + 2704
diagonal^2 = 17588

Taking the square root of both sides:

diagonal = √17588
diagonal ≈ 132.5

Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 132.5 mm. Rounded to the nearest tenth, the answer is 132.5 mm.