Fall asleep - slumber?

[varica]

English Language Tests, Intermediate level

ESL/EFL Test #122 "Sleep Expressions", question 3

Janine! Where were you? I've been looking all over for you. — Sorry, mom! I was reading a book by the tree over the lake, fell ......... and lost track of the time.

(a) sleep
(b) sleepy
(c) asleep
(d) slept

English Language Tests, Intermediate level

ESL/EFL Test #122 "Sleep Expressions", answer 3

Janine! Where were you? I've been looking all over for you. — Sorry, mom! I was reading a book by the tree over the lake, fell asleep and lost track of the time.

Correct answer: (c) asleep
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I couldn't help dozing off a few times,please explain the meaning of this sentence.and the word slumber.give some more examples of sentences by using slumber word,
thanks

[Alan]

Hi,

Your question:

[Saneta]

I've been looking all over for you= I've been looking everywhere for you?
all over= everywhere?

thanks

[Alan]

Yes.

Alan
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