You roll all the dice once. So if you had a 10d6 fireball you would roll 10d6 and apply that damage to all characters within the area of effect.
Core rule book under playing the game
Whenever a roll is required, the roll is noted as “d#,” with the “#” representing the number of sides on the die. If you need to roll multiple dice of the same type, there will be a number before the “d.” For example, if you are required to roll 4d6, you should roll four six-sided dice and add the results together
|j b 200|
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There is no RAW quote for the specific question you are asking. However the general practice is that an area of effect spell has a single damage roll that effects all targets.
Think of it as the specific Fireball produces a specific amount of damage to all creatures inside that Fireball (with reductions for saves etc). It also saves significant time at the table, since rolling 10d6 8 times can be time consuming and is unnecessary.
j b 200 has it right. When the rules set is put into practice in computer games, such as Temple of Elemental Evil, there is a separate roll for each affected creature. For the tabletop game, it's simplified as one roll for all, which is far easier for the GM to keep track of as well.
That's exactly why it's one damage roll applied to all creatures in the area of effect. No one wants to roll that many dice. It would just slow things down. Nothing in the reading of the damage of fireball, for example, indicates you should roll a new set of dice for every creature (and unattended object) in the area. It says it deals "1d6 points of fire damage per caster level (maximum 10d6) to every creature in the area." It's fairly well implied that you're only rolling those dice once.