Sorts and pga_aggregate_target

Hi All,
I am on Oracle v11.2.
I would like to verify my understanding of pga_aggregate_target here.
Query and plan of the same query shown below
SQL> select name, value from v$parameter where name like '%area_size' or name like 'pga%';
NAME                           VALUE
create_bitmap_area_size        8388608
bitmap_merge_area_size         1048576
hash_area_size                 131072
sort_area_size                 65536
pga_aggregate_target           2147483648
5 rows selected.
Elapsed: 00:00:00.11
SQL>
SQL> set autotrace on
SQL>
SQL> select * from ( select * from TABLE_A order by ap_first_inserted desc ) where rownum < 11 ;
                             ..... Output data ..........
10 rows selected.
Elapsed: 00:00:55.11
Execution Plan
Plan hash value: 712899093
| Id  | Operation               | Name         | Rows  | Bytes |TempSpc| Cost (%CPU)| Time     |
|   0 | SELECT STATEMENT        |              |    10 |   870 |       |   823K  (1)| 02:44:37 |
|*  1 |  COUNT STOPKEY          |              |       |       |       |            |          |
|   2 |   VIEW                  |              |    50M|  4199M|       |   823K  (1)| 02:44:37 |
|*  3 |    SORT ORDER BY STOPKEY|              |    50M|  2751M|  3876M|   823K  (1)| 02:44:37 |
|   4 |     TABLE ACCESS FULL   | TABLE_A      |    50M|  2751M|       |   122K  (1)| 00:24:30 |
Predicate Information (identified by operation id):
   1 - filter(ROWNUM<11)
   3 - filter(ROWNUM<11)
Statistics
          1  recursive calls
          0  db block gets
     446865  consistent gets
     446755  physical reads
          0  redo size
       1028  bytes sent via SQL*Net to client
        359  bytes received via SQL*Net from client
          2  SQL*Net roundtrips to/from client
          1  sorts (memory)
          0  sorts (disk)
         10  rows processedTABLE_A has 50 million records.
Am I correct in saying that, this query, mainly the SORT operation is completly executed in memory (stats after plan show "0" sorts (disk) ) ?
In the plan, under columns TempSpc, it shows "3876M". What is this? does that mean 3876 MB of space ? in that case it is much bigger than the 2GB pga_aggregate_target or it is 3876 million bytes (which is still 3 and half GB) ? if the size of data being sorted exceeds 2GB, will Oracle use disk space?
I checked in DBA_SEGMENTS, the data segment of TABLE_A has taken up about 3.5GB space.
Thanks in advance.

Thanks Jonathan.
So, basically due to the rownum filter, not much memory/disk space was used.
I ran another query which uses dense_rank function and it produced this stats
Statistics
       2631  recursive calls
      66486  db block gets
      44394  consistent gets
      54296  physical reads
   61478516  redo size
        775  bytes sent via SQL*Net to client
       4179  bytes received via SQL*Net from client
          4  SQL*Net roundtrips to/from client
          1  sorts (memory)
          1  sorts (disk)
    1006295  rows processedThere was 1 memory sort and 1 disk sort.
The parameters are like
SQL> select name, value from v$parameter where name like '%area_size' or name like 'pga%';
NAME                           VALUE
create_bitmap_area_size        8388608
bitmap_merge_area_size         1048576
hash_area_size                 10485760
sort_area_size                 10485760
pga_aggregate_target           0
5 rows selected.But this is a QA database.
The production database has parameters
SQL> select name, value from v$parameter where name like '%area_size' or name like 'pga%';
NAME                           VALUE
create_bitmap_area_size        8388608
bitmap_merge_area_size         1048576
hash_area_size                 131072
sort_area_size                 65536
pga_aggregate_target           2147483648
5 rows selected.Now, as the documentation says (v11.2), pga_aggregate_target parameter will be in effect in case of the prod database. Am I correct in saying that, if my query gets enough memory allocation from pga_aggregate_target (of 2GB), there should be no need of any disk sorting?

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