Average cube shadows

Like the post Integral of 1÷(x⁵+1), I was clickbaited on instagram with the following reel:

The question is quite simple again, what is the average area of a cube’s shadow when it is placed randomly?

I tried solving it with classic integrations, and happy to get it right, and learned randomly is actually kinda tricky to define :)

Also Alice’s solution in A tale of two problem solvers (Average cube shadows) is super awesome, maybe you should rest coding or debugging for a while, and watch the video :wink:

Here’s my solution hehe.