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
To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The height of the cylinder represents the vertical side, and the diameter represents the diagonal side.
Using the Pythagorean theorem, we can calculate the length of the diagonal side (longest straw) as follows:
Diagonal side = √(height^2 + diameter^2)
Diagonal side = √(122^2 + 52^2)
Diagonal side = √(14884 + 2704)
Diagonal side = √(17588)
Diagonal side ≈ 132.6 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm when rounded to the nearest tenth.
132.6 mm
To find the longest straw that can fit completely inside the juice can diagonally, we need to find the diagonal length of the cylinder.
First, let's find the length of the diagonal of the top face (lid) of the cylinder. Since the diameter of the can is 52 mm, the radius is half of that, which is 52/2 = 26 mm. Using the Pythagorean theorem, the diagonal length of the lid can be found by using the radius as two sides of a right triangle.
Applying the Pythagorean theorem, we have:
diagonal^2 = (radius^2 + radius^2)
diagonal^2 = (26^2 + 26^2)
diagonal^2 = (676 + 676)
diagonal^2 = 1352
Now, let's find the length of the diagonal of the side face of the cylinder. The height of the can is given as 122 mm. Using the Pythagorean theorem again, we can find the diagonal length of the side face by using the height as one side and the radius as another side of a right triangle.
Applying the Pythagorean theorem, we have:
diagonal^2 = (radius^2 + height^2)
diagonal^2 = (26^2 + 122^2)
diagonal^2 = (676 + 14884)
diagonal^2 = 15560
Next, let's find the diagonal length of the entire cylinder. Since the lid and side face are perpendicular to each other, we can consider the diagonal lengths of these two faces as two sides of a right triangle. By applying the Pythagorean theorem once more, we can find the diagonal length of the entire cylinder.
Applying the Pythagorean theorem, we have:
diagonal^2 = (diagonal^2 of lid + diagonal^2 of side face)
diagonal^2 = (1352 + 15560)
diagonal^2 = 16912
Now, to find the diagonal length of the cylinder, we take the square root of 16912:
diagonal = √16912
diagonal ≈ 130.1 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 130.1 mm.
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.