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That's going to depend on a lot of factors - including whether you squeeze out the water and how big the zucchinis are. I'd grab 3-4 good sized ones (8" maybe?) and then just keep track of how much is accumulating as you're doing the grating. Worst case scenario is you have leftover zucchini to do something with later.
One 3 lb zucchini
My calculation indicates somewhere around a pound or 2-3 medium sized zucchini based on 1 cup of grated weighs about 4 ounces. I don't have zucchini handy so I can't test it.
My guess is about 4 large zuke if you are using them in the winter and squeezing as much liquid as possible from them. In the summer they are much sweeter and removing as much water is not as necessary.
Plus a cherry on top if you pretty, pretty please.
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