If you don't know the keys being used in the array, how do you figure out which one you want the size of? Here's something that will tell you the echo out the sizes of all three dimensions.
count($arrayname); // First dimension
foreach($arrayname as $key=>$val)
{ count($val); // is the length of $arrayname[$key]
}
foreach($arrayname as $key=>$val)
{ foreach($val as $k2=>$v2)
{ count($v2); // is the length of $arrayename[$key][$k2]
}
}
Needless to say, that code won't do anything interesting, but you should be able to get the idea.