Question

a cylindrical tank of protective coating for aluminum has the height and diameter shown. a fence manufacturer dips strips of aluminum into the tank to cover them with the protective coating. 33.5 in. 22.5 in. what is the longest aluminum strip that the manufacturer can fit into the tank? round your answer to the nearest tenth. answer the longest aluminum strip that can fit into the tank is inches long

Explanation:

Step1: Identify the right - angled triangle

The height of the cylinder \(h = 33.5\) in and the diameter of the base \(d=22.5\) in. The longest length that can fit inside the cylinder is the length of the space - diagonal of the cylinder. The base diameter and the height of the cylinder form the two legs of a right - angled triangle, and the space - diagonal is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\) is \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 33.5\) and \(b = 22.5\).
\[c=\sqrt{33.5^{2}+22.5^{2}}\]
\[c=\sqrt{1122.25 + 506.25}\]
\[c=\sqrt{1628.5}\]
\[c\approx40.3547\]

Answer:

40.4 inches