Approximately 6” in diameter
This is a lidded porcelain box that may have been used for red paste ink (this is the kind of ink used when imporessing seals).
The cobalt glaze is typical of Chinese pottery, especially from the 20th century, for export markets. The dragon motif is done in a way that looks more modern, and in imitation of earlier painting. It is also less detailed and precise.
Based on sales of similar items, the Fair Market Value of this item is between $10 and $20.