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

To find the longest straw that can fit diagonally inside a cylindrical juice can, we can visualize it as the diagonal of a right triangle where the height of the cylinder serves as one leg of the triangle, and the diameter of the base provides a base leg when considering the diameter.

1. **Identify the dimensions of the cylinder**:
- Height (h) = 122 mm
- Diameter = 52 mm
- Radius (r) = Diameter/2 = 52 mm / 2 = 26 mm

2. **Find the diagonal (d) using the Pythagorean theorem**:
The diagonal of the cylinder will be the hypotenuse of the triangle formed by:
- The height (h = 122 mm)
- The diameter as its base (d = 52 mm)

However, for the diagonal, we need to calculate it across the circle formed by the cylinder's base:
\[
\text{Diagonal} = \sqrt{h^2 + d^2}
\]
Here, \(d\) will be the diameter, and it is equivalent to the diagonal between two opposite points on the circle's edge:
\[
d_{\text{circle}} = 2r = 52 \text{ mm}
\]

3. **Compute the diagonal length**:
\[
\text{Diagonal} = \sqrt{(122)^2 + (52)^2}
\]
\[
= \sqrt{14884 + 2704}
\]
\[
= \sqrt{17588}
\]
\[
\approx 132.6 \text{ mm}
\]

4. **Round to the nearest tenth**:
The longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.

Thus, the answer is **132.6 mm**.