Answer :
Final answer:
The distance covered by the minute hand from 10:10 am to 10:25 am is calculated by finding 1/4 of the circumference of the circle traced by the hand. Given that the minute hand is 84 cm long, the distance covered is 132 cm.
Explanation:
The question asks us to calculate the distance covered by the tip of the minute hand of a clock as it moves from 10:10 am to 10:25 am. The length of the minute hand is given as 84 cm.
First, we note that a clock is divided into 12 equal sections, so each section corresponds to 30 degrees as there are 360 degrees in a full rotation (360 degrees/12 sections = 30 degrees per section). From 10:10 to 10:25 am, the minute hand moves over 15 minutes, which is a quarter of the clock or 3 sections (since there are 60 minutes in an hour and the clock is divided into 12 sections). Therefore, the minute hand moves through an angle of 3 sections × 30 degrees/section = 90 degrees.
Now, the distance covered by the tip of the minute hand is part of the circumference of the circle formed by the minute hand's rotation. The formula for the circumference of a circle is C = 2πr. However, we only need the length of the arc that corresponds to 90 degrees (or ⅔ of the full circumference). So, we calculate ⅔ of the circumference: (⅔) × (2π × 84 cm) = ⅔ × (2 × 3.1416 × 84 cm) and this equals 132 cm.
Therefore, the correct answer to the question is C. 132 cm.
