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.what is the longest straw?
To find the length of 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 diagonal of a cylinder can be found using the Pythagorean theorem:
Diagonal length = √(height^2 + diameter^2)
Given that the height of the juice can is 122 mm and the diameter is 52 mm, we can calculate:
Diagonal length = √(122^2 + 52^2)
= √(14884 + 2704)
= √(17588)
≈ 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.
To find 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 the square of the hypotenuse (diagonal) of a right-angled triangle is equal to the sum of the squares of the other two sides.
In this case, the height of the cylinder (h) is one side of the right-angled triangle, and the diameter of the base (d) is the other side. Since the diameter is twice the radius (r), we can write the equation as follows:
diagonal^2 = h^2 + (2r)^2
First, we need to find the radius of the juice can by dividing the diameter by 2:
radius = diameter / 2 = 52 mm / 2 = 26 mm
Next, we can substitute the values into the equation to find the diagonal:
diagonal^2 = 122^2 + (2(26))^2
diagonal^2 = 14884 + 2704
diagonal^2 = 17588
To find the diagonal, we take the square root of both sides:
diagonal = √(17588) ≈ 132.6 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.
yay it's 132.6 thank you step-by-step bot.
To find the longest straw that can fit completely inside the juice can diagonally, we can use the concept of the Pythagorean theorem.
First, let's visualize the juice can as a cylinder. The height of the cylinder represents the vertical distance inside the can, while the diameter represents the maximum distance across the can.
To find the length of the diagonal, we need to calculate the hypotenuse of a right triangle formed by the height, the radius (which is half of the diameter) of the cylinder, and the length of the straw (which is the hypotenuse).
Step 1: Find the radius of the cylinder
The diameter is given as 52 mm, so the radius is half of the diameter: 52 mm / 2 = 26 mm.
Step 2: Set up the right triangle
The height of the cylinder is given as 122 mm, which forms one side of the right triangle. The radius of the cylinder forms the other side of the right triangle.
Step 3: Use the Pythagorean theorem
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
In this case, the hypotenuse represents the longest straw that can fit inside the juice can diagonally.
Using the formula, we have:
Hypotenuse^2 = Height^2 + Radius^2
Substituting the given values:
Hypotenuse^2 = (122 mm)^2 + (26 mm)^2
Step 4: Calculate the hypotenuse (longest straw)
Hypotenuse^2 = 14944 mm^2 + 676 mm^2
Hypotenuse^2 = 15620 mm^2
Taking the square root of both sides:
Hypotenuse = √(15620 mm^2)
Hypotenuse ≈ 124.9 mm (rounded to the nearest tenth)
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.9 mm.