Question

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. :)

Answer 1

thats not right

Answer 2

132.6

Answer 3

To find the length of the longest straw that can fit diagonally inside the cylindrical juice can, we can visualize the problem as finding the length of a diagonal inside a cylinder. The longest diagonal will stretch from one point on the base of the cylinder to the opposite point on the top face.

The diagonal, \(d\), inside a cylinder can be calculated using the formula derived from the Pythagorean theorem for a right triangle formed by the height of the cylinder and the diameter of the cylinder's base:

\[
d = \sqrt{h^2 + r^2}
\]

where:
- \(h\) is the height of the cylinder,
- \(r\) is the radius of the cylinder.

First, we need to find the radius of the base. Given the diameter is \(52\) mm, the radius \(r\) is:

\[
r = \frac{\text{diameter}}{2} = \frac{52 \, \text{mm}}{2} = 26 \, \text{mm}
\]

Now we can substitute the values into the formula. The height \(h\) is given as \(122\) mm.

Now we compute the diagonal \(d\):

\[
d = \sqrt{h^2 + r^2} = \sqrt{122^2 + 26^2}
\]

Calculating each squared term:

\[
122^2 = 14884 \quad \text{and} \quad 26^2 = 676
\]

Adding these values together:

\[
14884 + 676 = 15560
\]

Now, taking the square root to find \(d\):

\[
d = \sqrt{15560} \approx 124.0 \, \text{mm}
\]

Thus, the length of the longest straw that can fit completely inside the juice can diagonally is approximately:

\[
\boxed{124.0} \, \text{mm}
\]