Would liver cysts under 1cm light up if they were cancerous on a pet scan?

It may and may not: It depends. It may not light up if the size is smaller than 8mm to 10mm. So for small nodule- just because it is negative does not mean it completely rules out malignancy. Need to repeat imaging in close interval to ensure stability. ( if this is carcinoid that you are afraid of- octeotride scan can be helpful.).

See long answer: True liver cysts are simple fluid bubbles, are common and develop frequently with age. They usually aren’t associated with symptoms although there are some unusual conditions in which they occur. Pet-ct is usually for oncologic (cancer) concerns and detects metabolically active abnormal cells such as tumors. Benign liver cysts may be seen without activity on non pet ct portion of the exam.

No: Cyst by definition are benign fluid collections. Cystic masses , if cancerous , would probably "lite-up" . But my need an MRI for further evaluation.