Final answer:
The total angle the tires rotate through during the boy's trip is approximately 7500.24 radians.
Step-by-step explanation:
To find the total angle the tires rotate through during the boy's trip, we need to calculate the number of revolutions made by the tires. The circumference of a circle is given by the formula C = 2πr, where r is the radius and π is a constant value of approximately 3.14. In this case, the radius of the bicycle wheels is 30.0 cm, so the circumference is C = 2π(30.0 cm) = 60.0π cm.
To convert the distance the boy travels from kilometers to centimeters, we multiply the given distance by 100,000 since there are 100,000 centimeters in a kilometer. Therefore, the distance the boy travels in centimeters is 2.25 km × 100,000 cm/km = 225,000 cm.
The number of revolutions made by the tires can be calculated using the formula revolutions = distance / circumference. Substituting the known values, we get revolutions = 225,000 cm / (60.0π cm). Evaluating this expression, we find that the number of revolutions is approximately 1194.77 revolutions.
The total angle the tires rotate through, denoted by θ, can be found using the formula θ = 2π × revolutions. Substituting the value for revolutions, we get θ = 2π × 1194.77, which is approximately 7500.24 radians.