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)
The longest straw that can fit completely inside the juice can diagonally is equal to the space diagonal of the cylinder.
The space diagonal of a cylinder is the hypotenuse of a right triangle, where the height and diameter of the cylinder are the legs of the triangle.
Using the Pythagorean theorem, we can calculate the length of the space diagonal:
diagonal = sqrt(height^2 + diameter^2)
diagonal = sqrt(122^2 + 52^2)
diagonal = sqrt(14884 + 2704)
diagonal = sqrt(17588)
diagonal ≈ 132.6 mm
So the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.
To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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 diagonal of the juice can will act as the hypotenuse of a right-angled triangle, while the radius of the can will be one side, and the height of the can will be the other side.
First, we need to find the radius of the can by dividing the diameter by 2:
Radius = Diameter / 2 = 52 mm / 2 = 26 mm
Now, we can apply the Pythagorean theorem to find the length of the diagonal inside the can:
Diagonal^2 = Radius^2 + Height^2
Diagonal^2 = (26 mm)^2 + (122 mm)^2
Solving this equation will give us the square of the diagonal. To find the actual length of the diagonal, we take the square root of this value. Since we only need to round the answer to the nearest tenth, we can round at this step:
Diagonal ≈ √[(26 mm)^2 + (122 mm)^2]
Plugging in the values and solving the equation, we get:
Diagonal ≈ √[(676 mm^2) + (14,884 mm^2)]
Diagonal ≈ √(15,560 mm^2)
Diagonal ≈ 124.6 mm (rounded to the nearest tenth)
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.6 mm.
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 is the hypotenuse of a right triangle formed by the height, diameter, and the diagonal itself.
We can find the diagonal using the Pythagorean theorem:
diagonal² = height² + (diameter/2)²
diagonal² = 122² + (52/2)²
diagonal² = 14884 + 676
diagonal² = 15560
diagonal = √15560
diagonal ≈ 124.7 mm
Rounding to the nearest tenth, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm.