External HDD always spinning?

Hi all - looking for a bit of advice regarding my new setup...
I just got a 27" iMac, loving it so far, but curious about a possible issue with my external HDDs. I connected two external HDDs to it, one set up with Time Machine, and the other set up with Carbon Copy Cloner to back up once a day.

These are the HDDs I bought:
http://www.amazon.com/HGST-Deskstar-3-5-Inch-Internal-0S03086/dp/B004E9SGPY/ref=cm_cr_pr_product_top

And they're connected with these docks:
http://www.amazon.com/gp/product/B005UA3I72/ref=oh_details_o08_s00_i00

The issue is that the external drives are constantly spinning - not constantly reading/writing - just spinning non-stop. They're not 'working' drives, simply backups, so I figured they would only spin up when a backup is being performed, but that's not the case. It seems that it's an issue with the docks, because even with the drives ejected and the computer shut down, they still spin as long as the docks are powered on. They get pretty warm (borderline hot), so I've manually powered them off when I shut down - does anyone have any advice, or is this just a case of "it is what it is"?

My old setup was a late '09 21" iMac with two external Western Digital HDDs, and they didn't constantly spin like these new drives. Is this something I should worry about and/or return the docks and get different docks?

Also - somewhat unrelated question about the HDDs and the docks - since there are circuit boards exposed, should I worry about dust and other elements? They're in a fairly clean environment, but they're not enclosed in a case like a standalone external drive.

Thanks for any help or advice

Anybody have any input?

Thanks for the replies, guys. I do have the "Put hard disks to sleep when possible" option checked, but it doesn't seem to make a difference. I've dragged the drives to the trash, but they still spin even though they're unmounted. Whether the computer's on, sleeping, or completely shut down, it doesn't matter - in order for the drives to spin down I have to manually press the power button on the dock. And I do have iStat installed - I'm not sure how that's helpful in this situation though. I think I may just try getting some different docks and seeing if that helps at all...