Final answer:
The length of the trace of water left on the floor by the wet bicycle tire after making 3 full rotations is approximately 5.655 meters.
Step-by-step explanation:
To find the length of the trace of water left on the floor, we need to calculate the distance traveled by the wet bicycle tire. The tire makes 3 full rotations, which means it covers a distance equal to the circumference of the tire multiplied by 3. The circumference of the tire can be calculated using the formula C = 2πr, where r is the radius of the tire. Substituting r = 30 cm into the formula, we get C = 2π(30 cm). Converting the answer to meters, C ≈ 188.5 cm.
Since we have to multiply the circumference by 3, the total distance traveled by the tire is 3 × 188.5 cm ≈ 565.5 cm. Converting the distance from centimeters to meters, the trace of water left on the floor is approximately 5.655 meters.