A juice can is in the shape of a cylinder. It has a height of 122 mm in a diameter of 52 mm what is the longest straw that can fit completely inside the juice can diagonally? Around the answer to the nearest 10th
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.
First, let's find the length of the diagonal of the base of the cylinder. The diameter of the base is given as 52 mm, so the radius (r) of the base is half of that, which is 26 mm.
We can use the Pythagorean theorem to find the length of the diagonal (d) of the base:
d = √(2r^2) = √(2 * 26^2) = √(2 * 676) = √(1352) ≈ 36.7 mm
Next, we need to find the slant height of the cylinder. This is the height of the curved surface of the cylinder, which is the same as the height of the straw. The height of the cylinder is given as 122 mm.
Now, we can use the Pythagorean theorem again to find the length of the diagonal (D) of the cylinder:
D = √(d^2 + h^2) = √(36.7^2 + 122^2) = √(49.1369 + 14884) = √(14933.1369) ≈ 122.1 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 122.1 mm (rounded to the nearest 10th).
To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The diameter of the can is 52 mm, which means the radius is 52/2 = 26 mm.
The height of the can is 122 mm.
Let's consider the diameter of the straw to be the hypotenuse of a right triangle, with the height and radius of the can as the other two sides.
Applying the Pythagorean theorem:
Straw length^2 = height^2 + radius^2
Straw length^2 = 122^2 + 26^2
Straw length^2 = 14884 + 676
Straw length^2 = 15560
Straw length = √15560
Straw length ≈ 124.7 mm
Rounding to the nearest tenth gives us the longest straw length that can fit completely inside the juice can diagonally as approximately 124.7 mm.
To find the longest straw that can fit diagonally inside the juice can, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the cylinder can be imagined as a rectangular prism with a height (122 mm) and a diameter (52 mm), which means the radius is half the diameter, or 26 mm.
Let's consider the diagonal of the rectangular prism as the hypotenuse of the right triangle formed by the height, radius, and the diagonal itself.
We can calculate the length of the diagonal using the Pythagorean theorem:
Diagonal^2 = height^2 + radius^2
Plugging in the values, we get:
Diagonal^2 = 122^2 + 26^2
= 14884 + 676
= 15560
Taking the square root of both sides, we find:
Diagonal = √15560
≈ 124.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm. Rounded to the nearest tenth, the answer is 124.7 mm.