Pie is EverywhereCalculus Level 2
It is then shot straight into a very thick wall (i.e. it does not pierce the other side at all) making a closed cylindrical hole until it stops moving. Then the bullet is carefully extracted without affecting the hole at all, leaving an empty hole with a pointy end where the bullet once was.
The length of the entire hole is \(e+1\). If the volume of the hole can be expressed as \[\pi i e\] where \(i\) is a constant, find the value of \(i\).