I have a cylinder with an 8" radius. I want to build a hexagon box to cover it. How do I calculate the length of each side?

Knowing the radius is 8 inches, the length of a side of the hexagonal box would be

2tan(30)=9.24 \;\ \text{inches}

Make each side about 9 and a quarter inches long.

Also, see this thread:

https://www.askmehelpdesk.com/mathematics/formula-calculate-diameter-circle-within-hexagon-405154.html

By noting that the side length of the hexagon, L, in terms of the radius of the circle, R, is given by

L=\frac{2R}{\sqrt{3}}

This can be used to find any side length knowing the radius. Use yours.

L=\frac{16}{\sqrt{3}}=9.24.

Same as before.