Why using "in" preposition in the case?

Question

In the following sentence:

James made a hole in the bottom of a bucket.

Why using in preposition, while not talking about inside of an object?

Answer 1

Because in has many more meanings than inside of. (Whoever told you that in means inside of only told you half of the story. Check that – only told you about a tenth of the story!)

In their first definition of in, Cambridge lists several examples, including these:

Put the milk back in the fridge.
Is Mark still in bed?
I got stuck in a traffic jam for half an hour.
They live in a charming old cottage.
I've got a pain in my back.
How much is that coat on display in the window (= in the space behind the window of the shop)?
I've got something in (= on the surface of) my eye.

It's that last one that solves your mystery: the word in can be used to mean on the surface of. That's why we can say things like:

The iceberg cut a gash in the hull of the ship.
That pool table has a tear in the felt – no wonder they're only asking fifty dollars for it.
I just slipped in the mud; now I have a stain on my sleeve and a rip in my pants.
Dear Eliza, there's a hole in the bucket.