That looks like a seam, not a crack. The water is coming from the faucet. Granite is a porous, natural stone so it's not waterproof. It will not shield anything from constant water flow.

Yes, that is a seam in the granite. The water could be leaking through the seam or if the faucet did not have a good seal around the base to the granite, the water could have been leaking under the faucet seal and into the hole. Have a plumber install a new faucet, he will be able to tell you where it is leaking and should be able to fix it.

The granite is fine. The faucet is the problem. Talk to a plumber to get things dealt with.

jaspinner:

You aren't getting any substantial amount of water through those seams, I'll bet. You need to check how your sink is installed. I've reinstalled over 50 sinks due to fabricator error. Will a scraper or knife fit between the bottom of the stone and the sink flange anywhere? If so, the sink must be pulled, the flange cleaned, and sink reinstalled. Topical caulk is not an option.

If your top has been "rodded" or reinforced with the wrong steel and/or bedded in the wrong adhesive, this leaking sink can have catastrophic consequences if it causes the rod to oxidize, expand, and literally blow up the granite.

See if you can talk your plumber into installing the sink with a Hercules Universal Sink Harness (Braxton Bragg) or Sink Strap (Regent Stone Products). If it's the first one he's done, expect him to bill you for two hours; I can pull and restrap a sink in an hour and a quarter usually.

"Repaired" rod filled with polyester.

"Repaired" polyester lying next to the Grand Canyon of Oxidation.