10 gal rubbermaid mash tun for 10 gallon mash?

I have a 10 gallon rubbermaid cooler that I use as a mash tun. I've been using it for mashing 5 gallon batches, but just bought a bigger brew pot and want to do a 10 gallon batch. Will a 10 gallon rubbermaid cooler fit 24 lbs of malt with 9 gallons of strike water? Im afraid that it won't and don't want to risk screwing up my mash. For my 5 gallon cream ale recipe, I use 4.5 gallons of strike water so I figure that I should use 9 for a 10 gallon batch. If 9 gallons of water and 24 lbs of grain will not fit in the cooler, should I just mash twice (like i'm brewing two five gallon batches), or should I decrease the amount of strike water and increase the sparge amount? Im afraid if I decrease the strike water amount and increase the sparge water amount that it will not produce the same results. Is this assumption correct? Any advice would help. Thanks.

Check this out.
http://www.rackers.org/calcs.shtml

Oh wow, this is awesome. Thanks alot.

Ok, well that answered my main question. But now I have another question. My 5 gallon recipe called for 1.6 qt/lb of strike water. According to the calculator provided in the link above, I would have to lower my strike amount to 1.3 or 1.2 qt/lb to be able to fit it in my mash tun. I would then componsate by adding more sparge water. If I decide to do this, how will it affect my results? Will the taste change, will the gravity change?

Probably not. Kaiser has some experimental data on his site that show a very minimal change in fermentability with mash thickness.

should be fine, just beware that when you've got the mash tun that full it's really easy to make a mess when you're trying to get those last few pounds of grain into the mash.

Here's 16 lbs of grist with 6 gal water in a 7.5 gal lauter tun/stock pot look like.
I direct heat the mash in a 9 gal kettle and ladle to this lauter tun. I don't have to add water to raise temperature....

I mash up to 26 pounds of grain in my 10 gallon cooler using a 1 to 1 ratio. Have to split my sparge into 2 but it works great.