[condition] + 岂不是 + [conclusion]?
[condition] + 岂不 + [adjective / verb]?
岂不是 asks "wouldn't that be…?" without wanting an answer. 岂 is the written "how could", so 岂不是 means "how could it not be": the speaker is pointing out a conclusion that follows from what was just said. It usually comes after a condition or after 这样.
The conclusion is often unwelcome, so 岂不是 works as a warning or an objection.
Before an adjective or a verb, 是 can drop. 岂不 + adjective is the more written of the two.
Without 不, 岂 denies: 岂是 "is by no means", 岂能 "how could one". 这岂是小事 says it is no small matter; 这岂不是小事 would say it obviously is one.
岂不是 already knows the answer. For a question you actually want answered, use 是不是 or 吗.