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)
mm
check answer remaining attempts : 3

Explanation:

Step1: Find radius of the base

The diameter is 52 mm, so radius $r = \frac{52}{2} = 26$ mm.

Step2: Calculate base diagonal

Use Pythagoras for the circular base (diameter is the diagonal of the square that encloses the circle, which is the horizontal distance we need for the space diagonal). The horizontal diagonal across the base is the diameter, 52 mm.

Step3: Calculate space diagonal

Use 3D Pythagorean theorem: space diagonal $d = \sqrt{h^2 + d_{base}^2}$, where $h=122$ mm, $d_{base}=52$ mm.
$$d = \sqrt{122^2 + 52^2}$$
$$d = \sqrt{14884 + 2704}$$
$$d = \sqrt{17588} \approx 132.6$$

Answer:

132.6 mm