How much wood does a woodchuck chuck?

Normally, the duct is cylindrical, although this is not mandatory, and of a diameter suitable for the volumetric flow rate (CFM) of the hood to cause a duct velocity between 1000 and 2000 ft/min. Obviously, this depends on the hood when it comes with a blower, and depends on intake area velocity rules when one is choosing a blower independent of the hood.

So, you will need to specify your hood parameters to answer the question. You could, alternatively, choose a hood on some basis, and read its installation instructions, usually available for download.

A quick search of 30" and 36" under-cabinet range hoods on build.com returned 356 products. The top four duct sizes for vertical exhaust were 3-1/4"x10" (150), 7" round (143), 6" round (88), and 8" round (75).

It depends on the hood you select. Our under cabinet hood specified a 10" round duct. Fits fine.