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> もしたくさんの遺産があったとしたらどのように **使うのですか？**
>
> Say if it so happened that you had a lot of inheritance, how would you use
> it?

versus

> 仮に、お金が一億円あるとしたら、何に **使いますか。**
>
> If you were to have 100 million yen for instance, what would you use it for?

In the former sentence, のですか is used, while in the latter just か is used.

**Question:** Why is のですか used in one and not the other?

I was taught that のですか is appropriate to use when seeking specific information
to fill a gap in knowledge. It seems that a direct question (like in the
second sentence) qualifies as that. So why does it lack the 「のですか」?
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questions
か vs. のですか in Hypothetical Question Sentences
First, 使うのですか is too polite compared to 使いますか.  
使うんですか is better to say unless you're a butler.

使うんですか feels like you've already mentioned the thing or you know the listener
knows the thing. 使いますか can be used in more situations, and you can almost
always replace 使うんですか with 使いますか。

もしたくさんの遺産があったとしたらどのように使うんですか？ would be used when you're already talking about
the inheritance. And 使いますか can be used in the same situation.

もしたくさんの遺産があったとしたらどのように使いますか？ can be used when you just want to know the answer
and try asking it too.
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This type of の for seeking clarification is generally not used with purely
hypothetical questions that have nothing to do with the reality. There is
usually no need to "wonder about someone's intention" for such questions.

  1. 仮にお金が1億円あるとしたら、何に使いますか？
  2. 仮にお金が1億円あるとしたら、何に使うのですか？

Sentence 1 is a natural what-if question you can ask casually for fun.

Sentence 2 sounds rather sudden when said without any prior context. It sounds
like the speaker has some actual concern about a millionaire's (or the
listener's) mindset. However, it would sound natural after sufficient context
has been established, as in the following examples:

  * 私には大きなお金の使い方がわかりません。仮にお金が1億円あるとしたら、何に使うのですか？  
I have no idea how to spend a lot of money. What does someone spend it on if
they have 100 million yen?  
(The speaker has doubt about a millionaire's mindset in general.)

  * え？ 今すぐ1億円が欲しい？ 仮にお金が1億円あるとしたら、何に使うのですか？  
Huh? You need 100 million yen right now? Even if you had it, what would you
spend it on?  
(The speaker wants to clarify the speaker's intention.)

The same goes for your first example about 遺産. It sounds like a nuanced
question to me.
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