Crossword Genius

Consumed amount of mint cake after leadership spill (6)

Ross

I believe the answer is:

intake

I'm a little stuck... Click here to teach me more about this clue!

'cake after leadership spill' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps you can see a link between them that I don't see?

'consumed amount of mint' is the wordplay.
I cannot quite understand how this works, but
'amount' could be 'take' (take is a kind of amount) and 'take' is present in the answer.
The remaining letters 'in' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for intake that I've seen before include "(Quantity of) new students accepted by school" , "Place where gas or water enters" , "New recruits" , "Air inlet of jet engine" , "Consumption" .)

I've seen this clue in the Sydney Morning Herald.
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