Final answer:
The distance the tip of the second hand travels in 45 seconds is approximately 47.12 cm when rounded to the nearest 100th, calculated by finding the proportion of the circle's circumference that corresponds to 45 seconds.
Step-by-step explanation:
The tip of the second hand of a clock describes a circle as it moves, with the length of the second hand being the radius of the circle. To find the distance the tip travels in 45 seconds, we calculate the circumference of the circle and then find the proportion of the circumference that corresponds to 45 seconds.
Step by Step Calculation
- Calculate the circumference of the circle: Circumference = 2 × π × radius. Here, the radius (r) is 10 cm. Circumference = 2 × π × 10 cm = 20π cm.
- Since the second hand makes a full rotation in 60 seconds, the distance traveled in 45 seconds is ⅔ of the full circumference.
- Distance traveled in 45 seconds = ⅔ × 20π cm = 15π cm.
- Calculate the value of 15π cm. Approximately, 15π ≈ 15 × 3.14159 ≈ 47.12 cm.
- Round the distance to the nearest 100th: 47.12 cm.
Therefore, the distance the tip of the second hand travels in 45 seconds is approximately 47.12 cm when rounded to the nearest 100th.