Question

bruce wants to ship a fishing pole to his brother. the longest cylinder - shaped container available for shipping has a diameter of 13 in. and a height of 84 in. what is the longest fishing pole bruce can ship to his brother? the longest fishing pole can be in. long. check answer remaining attempts : 2 view previous attempt

Explanation:

Step1: Find the diagonal of the base

The diameter of the base \(d = 13\) in. The base is a circle, and if we consider the right - triangle formed by the diameter of the base and the height of the cylinder for the space - diagonal (longest distance inside the cylinder), first, the base diagonal \(b=13\) in (since for a circle, the longest straight - line distance across the base is the diameter).

Step2: Apply the three - dimensional Pythagorean theorem

The formula for the space - diagonal \(l\) of a cylinder (using the Pythagorean theorem in 3D, similar to a rectangular prism where one side is the diameter of the circular base) is \(l=\sqrt{b^{2}+h^{2}}\), where \(b\) is the diagonal of the base and \(h\) is the height of the cylinder. Given \(b = 13\) in and \(h=84\) in.

$$l=\sqrt{13^{2}+84^{2}}=\sqrt{169 + 7056}=\sqrt{7225}$$

Step3: Calculate the square root

Since \(85\times85 = 7225\), \(\sqrt{7225}=85\)

Answer:

\(85\)