Socially assistive robots (SARs) are increasingly deployed in educational and information-sharing contexts, supported by advances in large language models that enable fluent real-time interaction. Despite the growing diversity of robot embodiments, it remains unclear whether a single robot appearance is appropriate across different interaction tasks or whether trust depends primarily on contextual factors. In this study, we examine how robot appearance and task type jointly influence trust in robots. Using a within-subjects video-based experiment (N = 81), participants evaluated three robots with distinct appearances while performing three educationally relevant tasks: teaching, procedural instruction, and personal-information discussion. Results from repeated-measures analyses show a strong main effect of task on trust, with participants reporting the highest trust during instructional guidance, moderate trust during teaching activities, and significantly lower trust when robots requested personal information. In contrast, robot appearance showed no significant main effect, and the interaction between appearance and task was marginal. These findings suggest that trust in human-robot interaction is shaped more strongly by task context than by physical embodiment alone. By focusing on future educators as end users, this work contributes empirical evidence toward task-aware robot deployment in educational environments and highlights the importance of aligning robot roles and behaviors with interaction goals rather than relying solely on anthropomorphic design.