To find the length of the straw that fits diagonally from the bottom left corner to the top right back corner of a rectangular box, we can use the three-dimensional version of the Pythagorean theorem.
Given the dimensions of the box:
- Length \( l = 6 \) inches
- Width \( w = 6 \) inches
- Height \( h = 1 \) inch
The formula for the diagonal \( d \) of a rectangular box in three dimensions is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Substituting the given dimensions into the formula:
\[ d = \sqrt{6^2 + 6^2 + 1^2} \]
Calculating each term:
\[ 6^2 = 36, \quad 6^2 = 36, \quad 1^2 = 1 \]
Now, sum these values:
\[ d = \sqrt{36 + 36 + 1} = \sqrt{73} \]
Thus, the length of the straw is:
\[ \boxed{\sqrt{73}} \text{ inches} \]
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