Final answer:
To calculate the number of rotations, we find the circumference of the bicycle's wheel using its diameter and divide the total distance (converted to centimeters) by the wheel's circumference. The wheels with a diameter of 64 cm will make approximately 2485 rotations when the bicycle travels 5 km, which does not match any of the given answer options.
Step-by-step explanation:
To determine how many rotations a bicycle wheel makes when traveling a certain distance, you can use the relationship between the circumference of the wheel and the distance traveled. The formula to find the circumference (C) of a circle (which is the distance the bike travels in one rotation of the wheel) is C = π × diameter. With a wheel diameter of 64 cm, the circumference of the wheel is C = π × 64 cm.
Next, we convert the travel distance from kilometers to centimeters because the wheel's diameter is given in centimeters. There are 100,000 centimeters in a kilometer, so for 5 kilometers, the total distance in centimeters is 5 km × 100,000 cm/km = 500,000 cm. To calculate the number of rotations, divide the total distance traveled by the circumference of the wheel:
Number of rotations = Total distance traveled / Circumference
Number of rotations = 500,000 cm / ( π × 64 cm )
Use the value of π (approximately 3.14159) to calculate the number of rotations and round to the nearest whole number. After the calculations, we find that the wheels will make approximately 2485 rotations. Hence, none of the answer options given (a. 39 rotations, b. 40 rotations, c. 41 rotations, d. 42 rotations) are correct.