115982 is a very similar question
Is this a 64bit server - do you have the lock pages in memory local policy enabled?
the most likely reason is that this SQL Server 64bit instance is using “locked pages” as I’ve described in an earlier question. Notice the name on the Task Manager column is called Memory (Private Working Set). Remember we also said that if SQL Server 64bit instances use “locked pages” this memory would not be part of the working set (because remember AWE APIs are used on 64bit to “lock” pages and that memory is not part of the working set). So since the locked pages are not part of the working set, they won’t appear in this column in Task Manager. On the Task Manager for Windows Server 2003, this column is called “Mem Usage” but it also reflects the working set of the process.
Here is an article that explains it in depth
You can also view the counters in SQL
,ROUND(( cntr_value * 8192.0 ) / 1048576, 0) AS cntr_value_MB
object_Name LIKE '%Buffer Manager%'
AND RTRIM(counter_name) IN ( 'Free pages', 'Total pages',
'Database pages' )
,ROUND(( cntr_value / 1024 ), 0) AS cntr_value_MB
counter_name IN ( 'Target Server Memory (KB)',
'Total Server Memory (KB)' )