Final answer:
To find how many times a 26-inch diameter bicycle wheel rolls in 200 feet, calculate the wheel's circumference in feet and divide 200 by this number, resulting in approximately 29.39 revolutions.
Step-by-step explanation:
To determine how many times a bicycle wheel of diameter 26 inches rolls as it travels 200 feet, we first calculate the circumference of the wheel. The circumference (C) is the distance around the wheel, and we use the formula C = πd, where d is the diameter of the wheel, and π (pi) is approximately 3.14159. In this case, the diameter is 26 inches, so:
C = 3.14159 × 26 inches ≈ 81.68 inches.
Since there are 12 inches in a foot, we convert the circumference to feet:
C ≈ 81.68 inches ÷ 12 inches/foot ≈ 6.807 feet per revolution.
Now, to find the number of revolutions (R) for a distance of 200 feet, we divide the total distance by the circumference:
R = 200 feet ÷ 6.807 feet/revolution ≈ 29.39 revolutions.
The bicycle wheel rolls approximately 29.39 times as it travels 200 feet.