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 str that can fit completely inside the juice can diagonally round answer to the nearest tenth
To find the longest straight line that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The diagonal of the juice can can be found by using the height and diameter as the two perpendicular sides of a right triangle. We can calculate the diagonal length (d) using the formula:
d = sqrt(h^2 + (d/2)^2)
where h = height of the cylinder and d = diameter of the cylinder.
Plugging in the values:
d = sqrt(122^2 + (52/2)^2)
d = sqrt(14884 + 676)
d = sqrt(15560)
d ≈ 124.7 mm
Therefore, the longest straight line that can fit completely inside the juice can diagonally is approximately 124.7 mm.
wrong
My apologies for the error in my previous response. Let me correct that.
To find the longest straight line that can fit completely inside the juice can diagonally, we can consider the diameter of the base of the cylinder as the hypotenuse of a right triangle, where the height of the cylinder and the radius (half the diameter) of the base are the other two sides.
Using the Pythagorean theorem:
Diagonal length = sqrt((radius)^2 + height^2)
Given that the diameter is 52 mm, the radius is 26 mm.
Diagonal length = sqrt(26^2 + 122^2)
Diagonal length = sqrt(676 + 14884)
Diagonal length = sqrt(15560)
Diagonal length ≈ 124.6 mm
Therefore, the longest straight line that can fit completely inside the juice can diagonally is approximately 124.6 mm.
wrong tell me the right answer pls
I apologize for the confusion in my previous responses. Let's recalculate the diagonal length of the juice can correctly.
Given:
Height (h) = 122 mm
Diameter (d) = 52 mm
Radius (r) = d/2 = 26 mm
Using the Pythagorean theorem:
Diagonal length = sqrt(r^2 + h^2)
Substitute the values:
Diagonal length = sqrt(26^2 + 122^2)
Diagonal length = sqrt(676 + 14884)
Diagonal length = sqrt(15560)
Diagonal length ≈ 124.6 mm
Therefore, the correct answer is that the longest straight line that can fit completely inside the juice can diagonally is approximately 124.6 mm.