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)
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 can be found by using the Pythagorean Theorem, which states that the square of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the height of the cylinder (122 mm) is one side of the right triangle, and the radius (half the diameter) is the other side. We can find the radius by dividing the diameter (52 mm) by 2.
Radius = Diameter / 2
Radius = 52 mm / 2
Radius = 26 mm
Now, we can find the diagonal using the Pythagorean Theorem:
Diagonal^2 = Height^2 + Radius^2
Diagonal^2 = (122 mm)^2 + (26 mm)^2
Diagonal^2 = 14884 mm^2 + 676 mm^2
Diagonal^2 = 15560 mm^2
To find the length of the diagonal, we take the square root of both sides:
Diagonal = √(15560 mm^2)
Using a calculator, the diagonal is approximately 124.9 mm.
Therefore, the longest straw that can fit completely inside the juice can diagonally is 124.9 mm (rounded to the nearest tenth).
To find the longest straw that can fit completely inside the juice can diagonally, we need to calculate the diagonal of the cylinder.
The diameter of the cylinder is given as 52 mm, which means the radius is half of the diameter, so the radius is 52/2 = 26 mm.
To find the diagonal, we can imagine a right triangle formed by the height, radius, and diagonal. The height forms the vertical side of the triangle, the radius forms the horizontal side, and the diagonal forms the hypotenuse.
Using the Pythagorean theorem, we can calculate the diagonal as follows:
diagonal^2 = height^2 + radius^2
diagonal^2 = 122^2 + 26^2
diagonal^2 = 14884 + 676
diagonal^2 = 15560
Taking the square root of both sides, we get:
diagonal = √15560
diagonal ≈ 124.9 mm
Rounding this to the nearest tenth, the longest straw that can fit completely inside the juice can diagonally is approximately 124.9 mm.
thats wrong
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 radius of the cylinder.
First, we need to find the radius of the cylinder.
The diameter is given as 52 mm, so the radius is half of that, which is 52/2 = 26 mm.
Now, we can use the Pythagorean theorem to find the diagonal of the cylinder.
The height (H) is one leg of the right triangle, and the radius (r) is the other leg.
The diagonal (D) is the hypotenuse of the right triangle.
Using the Pythagorean theorem: D² = H² + r²
D² = 122² + 26²
D² = 14,884 + 676
D² = 15,560
Taking the square root of both sides:
D ≈ √15,560
D ≈ 124.8 mm
Rounding to the nearest tenth:
D ≈ 124.8 mm
So, the longest straw that can fit completely inside the juice can diagonally is approximately 124.8 mm.