Final answer:
To determine how many times the pebble touches the ground, the circumference of the bicycle tire was calculated and the distance traveled was divided by this value, resulting in approximately 346 touches.
The correct option is C
Step-by-step explanation:
The question asks how many times the pebble touches the ground as a bicycle with a tire radius of 46 cm travels 1 km. To answer this, we calculate the circumference of the tire which is the distance the bike travels for one complete rotation of the tire.
The circumference (C) of the tire is given by the formula C = 2πr, where π (pi) is approximately 3.1416 and r is the radius of the tire. Thus, the circumference of the tire is C = 2 × 3.1416 × 46 cm. This equals to approximately 289.1 cm per revolution.
To find out how many revolutions the tire makes when the bicycle travels 1 km, we convert 1 km to centimeters (1 km = 100,000 cm), and then divide by the circumference of the tire:
Number of revolutions = Distance traveled / Circumference of tire
Number of revolutions = 100,000 cm / 289.1 cm/rev
Number of revolutions ≈ 346 revolutions
Therefore, the pebble touches the ground approximately 346 times when the bicycle travels 1 km.
The correct option is C