This study investigates the effects of culture, robot appearance and task on human-robot interaction. We propose a model with culture (Chinese, Korean and German), robot appearance (anthropomorphic, zoomorphic and machinelike) and task (teaching, guide, entertainment and security guard) as factors, and analyze these factors' effects on the robot's likeability, and people's active response to, engagement with, trust in and satisfaction with the robot. We conducted a laboratory experiment with 108 participants to test the model and performed Repeated ANOVA and Kruskal Wallis Test on the data. The results show that cultural differences exist in participants' perception of likeability, engagement, trust and satisfaction; a robot's appearance affects its likeability, while the task affects participants' active response and engagement. We found the participants expected the robot appearance to match its task only in the interview but not in the subjective ratings. Interaction between culture and task indicates that participants from low-context cultures may have significantly decreased engagement when the sociability of a task is lowered. We found strong and positive correlations between interaction performance (active response and engagement) and preference (likeability, trust and satisfaction) in the human-robot interaction.