Final answer:
The minute hand of a clock turns through 4/5π radians in 24 minutes.
Step-by-step explanation:
To determine the number of radians the minute hand of a clock turns in 24 minutes, we need to find the fraction of a complete revolution represented by 24 minutes. In one hour, or 60 minutes, the minute hand makes a complete revolution of 2π radians. Therefore, in 24 minutes, the minute hand turns through (24/60) times a complete revolution, or (24/60) * 2π radians.
Simplifying the expression, we have (24/60) * 2π = (4/10) * 2π = (2/5) * 2π = 4/5π radians.
So, the minute hand of a clock turns through 4/5π radians in 24 minutes.