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A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30cm, and the bicycle wheel makes 3 full rotations before stopping. How long is the trace of water left on the floor? Round your answer to the nearest cm. cm

A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 cm 30 \mathrm{~cm} , and the bicycle wheel makes 33 full rotations before stopping.\newlineHow long is the trace of water left on the floor?\newlineRound your answer to the nearest cm \mathrm{cm} .\newline□\square cm

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Full solution

Q. A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 cm 30 \mathrm{~cm} , and the bicycle wheel makes 33 full rotations before stopping.\newlineHow long is the trace of water left on the floor?\newlineRound your answer to the nearest cm \mathrm{cm} .\newline□\square cm
  1. Calculate Circumference: Calculate the circumference of the tire using the formula C=2⋅π⋅rC = 2 \cdot \pi \cdot r, where rr is the radius.\newlineC=2⋅π⋅30 cmC = 2 \cdot \pi \cdot 30 \, \text{cm}\newlineC=60π cmC = 60\pi \, \text{cm}
  2. Determine Total Length: Determine the total length of the trace by multiplying the circumference by the number of rotations.\newlineTotal length = C×number of rotationsC \times \text{number of rotations}\newlineTotal length = 60π cm×360\pi \, \text{cm} \times 3\newlineTotal length = 180π cm180\pi \, \text{cm}
  3. Convert to Rounded Value: Convert the exact length to a rounded value to the nearest centimeter.\newlineTotal length ≈180×3.14\approx 180 \times 3.14 cm\newlineTotal length ≈565.2\approx 565.2 cm\newlineRound to the nearest cm: 565565 cm

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