West's diamond pre-empt certainly serves it is purpose, you do not know where the ♣K is, the only card you need to bid and make slam.  However, there is an age-old technique - bid it and find out later where the king is.

East’s ♦2 confirms the diamonds are breaking 7-1.  (He would play Hi-Lo with 2 cards)

If East holds three trumps and the ♣K, both of which are quite likely, you will be able to endplay him. 

You win the diamond lead and play the A and K of trumps.  You play the ♠A and then lead the two of trumps, throwing East in.  Like it or not, he must now give you an entry to dummy.  You have sacrificed one trick to gain two tricks in return.  If East exits with a spade, you will score the Jack and King of the suit, allowing you to throw two minor suit losers.  If East plays a club instead, this will spare you a club loser and you can throw your remaining diamond on the ♠K.

Why is it likely that East held three trumps?
A pre-emptor usually holds a singleton somewhere.  When it is a side suit singleton, he will often lead it.  West's actual diamond lead suggested that his singleton would be in the trump suit.  Also of course, he is more likely to have a singleton in a suit where you hold nine cards between the combined hands than in one where you hold six cards.

An extract from TEST YOUR BRIDGE TECHNIQUE – Entry Management by David Bird and Tim Bourke.  isbn 9781894154758 00000 Master Point Press