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. (1 point)

Answer 1

its wrong

Answer 2

To find the longest straw that can fit completely inside the cylindrical juice can diagonally, we can think of the straw as a diagonal line that runs from one point on the bottom circle of the cylinder to the opposite point on the top circle.

We can use the Pythagorean theorem in three dimensions. The diagonal \(d\) of the cylinder can be calculated using the formula:

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

where \(h\) is the height of the cylinder and \(r\) is the radius of the base of the cylinder. The radius \(r\) is half the diameter.

Given:
- Height \(h = 122\) mm
- Diameter \(d = 52\) mm, thus the radius \(r = \frac{52}{2} = 26\) mm.

Now we can substitute the values into the formula for the diagonal:

\[
d = \sqrt{h^2 + 2r^2}
\]
\[
d = \sqrt{122^2 + 2 \cdot 26^2}
\]
\[
= \sqrt{14884 + 2 \cdot 676}
\]
\[
= \sqrt{14884 + 1352}
\]
\[
= \sqrt{16236}
\]
\[
= 127.4 \text{ mm (rounded to the nearest tenth)}
\]

Thus, the longest straw that can fit completely inside the juice can diagonally is approximately **127.4 mm**.