indulge (someone's) curiosity

Translations
удовлетворять (чьё-то) любопытство
The teacher indulged the students' curiosity by answering all their questions.
Учитель удовлетворил любопытство учеников, ответив на все их вопросы.
Definitions
To satisfy or fulfill someone's desire to learn or know more about a particular subject or topic.