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)
To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
First, we need to find the length of the diagonal of the top of the cylinder. The diagonal of a rectangle can be found using the formula:
diagonal = √(length^2 + width^2)
Since the diameter is equal to the width of the top of the cylinder, the length is equal to the diameter. Therefore, the length of the diagonal of the top is:
diagonal_top = √(52mm^2 + 52mm^2) = √(2704mm^2) = 52 mm
Next, we need to find the length of the diagonal of the height of the cylinder. The diagonal of a rectangle can be found using the formula mentioned earlier:
diagonal = √(height^2 + width^2)
Here, the height is perpendicular to the diameter, so the length is equal to the height of the cylinder. Therefore, the length of the diagonal of the height is:
diagonal_height = √(122mm^2 + 52mm^2) = √(15904mm^2) = 126.1 mm
Since the straw needs to fit completely inside the juice can diagonally, the longest straw that can fit completely inside is the smaller length, which is 52 mm.
Therefore, the longest straw that can fit completely inside the juice can diagonally is 52 mm.
Incorrect
To find the longest straw that can fit completely inside the juice can diagonally, we need to find the diagonal of the juice can.
The diagonal of a cylinder can be found by using the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the height, diameter, and the diagonal itself.
Using the Pythagorean theorem, we can calculate the diagonal:
diagonal = √(height^2 + diameter^2)
diagonal = √(122mm^2 + 52mm^2) = √(14944mm^2) = 122.2 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 122.2 mm.
Incorrect again
Apologies for the previous incorrect responses.
To find the longest straw that can fit completely inside the juice can diagonally, we can consider the height, diameter, and diagonal of the juice can as the three sides of a right triangle.
The diameter of the juice can is the base of the right triangle, the height is the perpendicular side, and the diagonal is the hypotenuse.
Using the Pythagorean theorem, we can find the length of the diagonal:
diagonal = √(height^2 + diameter^2)
diagonal = √(122mm^2 + 52mm^2)
diagonal = √(14784mm^2)
diagonal ≈ 121.6 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 121.6 mm.
The correct answer is 132.6
Apologies for the previous incorrect responses.
To find the longest straw that can fit completely inside the juice can diagonally, we can consider the height, diameter, and diagonal of the juice can as the three sides of a right triangle.
The diameter of the juice can is the base of the right triangle, the height is the perpendicular side, and the diagonal is the hypotenuse.
Using the Pythagorean theorem, we can find the length of the diagonal:
diagonal = √(height^2 + diameter^2)
diagonal = √(122mm^2 + 52mm^2)
diagonal = √(14944mm^2)
diagonal ≈ 122.4 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 122.4 mm.