Question

marc commutes to work on his bicycle, which has tires that measure 26 inches in diameter. a device on his bike informs him that one tire completed 388 full rotations between the time he left his house and the time he arrived at work. rounded to the nearest inch, how far did marc bike between his house and work?10,088 in.15,846 in.31,692 in.63,385 in.

Explanation:

Step1: Find tire circumference

The circumference \( C \) of a circle is \( C = \pi d \), where \( d = 26 \) inches.
\( C = \pi \times 26 = 26\pi \) inches

Step2: Calculate total distance

Multiply circumference by number of rotations (388).
\( \text{Total Distance} = 26\pi \times 388 \)
Substitute \( \pi \approx 3.1416 \):
\( \text{Total Distance} \approx 26 \times 3.1416 \times 388 \approx 81.6816 \times 388 \approx 31,692 \) inches

Answer:

31,692 in.