Question

a straw is placed inside a rectangular box that is 9 inches by 6 inches by 8 inches, as shown. if the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? leave your answer in simplest radical form.
answer

Explanation:

Step1: Use space diagonal formula

The formula for the space diagonal \(d\) of a rectangular prism with length \(l\), width \(w\), height \(h\) is \(d = \sqrt{l^2 + w^2 + h^2}\). Here, \(l=9\) in, \(w=6\) in, \(h=8\) in.

Step2: Calculate squared dimensions

\(9^2 = 81\), \(6^2 = 36\), \(8^2 = 64\)

Step3: Sum the squared values

\(81 + 36 + 64 = 181\)

Step4: Take square root of the sum

\(d = \sqrt{181}\)

Answer:

\(\sqrt{181}\) inches