Question

the pythagorean theorem in three dimensions practice
complete this assessment to review what youve learned. it will not count toward your grade.
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 the diagonal of the base

The base is a circle. The diameter \(d = 52\) mm. Using the Pythagorean theorem for the base (a circle's diameter - if we consider a right - angled triangle in the base plane, for a circle, the maximum length in the base plane is the diameter). Let \(a = 52\) (diameter of the base) and \(b=122\) (height of the cylinder).
The formula for the space diagonal \(l\) of a cylinder (using the three - dimensional Pythagorean theorem \(l=\sqrt{a^{2}+b^{2}}\))

Step2: Calculate the space diagonal

Substitute \(a = 52\) and \(b = 122\) into the formula \(l=\sqrt{52^{2}+122^{2}}\).
First, calculate \(52^{2}=52\times52 = 2704\) and \(122^{2}=122\times122=14884\).
Then \(a^{2}+b^{2}=2704 + 14884=17588\).
Now, \(l=\sqrt{17588}\approx132.6\)

Answer:

\(132.6\)