saswata4s wrote:

Johan rides his bicycle to and from college everyday, and the round trip takes 2 hours. If the radius of the front wheel is 30 cm and the wheel makes 30000 rotations over the course of round trip, then which of the following is closest to Johan's average speed?

(A) 2π km/hr

(B) 4π km/hr

(C) 9π km/hr

(D) 10π km/hr

(E) 12π km/hr

The total distance of the round trip is equal to the circumference of the wheel times the number of rotations over the course of the round trip. Since the radius of the wheel is 30 cm, the circumference is C = 2πr = 2 x π x 30 = 60π cm. Since the wheel makes 30,000 rotations over the course of the round trip, the total distance of the round trip is 60π x 30,000 = 1,800,000π cm. Since the round trip takes 2 hours and rate = distance/time, the rate is 1,800,000π/2 = 900,000π cm/hr.

Now we need to convert cm to km. Since 1 m = 100 cm, 900,000π cm = 9,000π m. Since 1 km = 1,000 m, 9,000π m = 9π km. Thus, the rate is 9π km/hr.

Answer: C

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