Question

derive and apply formulas for circumference

1. math on the spot a counter recorded 254 revolutions of the bicycle wheel shown. how far did the bicycle travel? use $\frac{22}{7}$ for $pi$.

a. how far does the wheel roll for one tire revolution?
b. what is the total distance recorded?
diameter $\frac{5}{4}$ ft

Explanation:

Step1: Find wheel circumference (1 revolution)

The distance for one revolution is the circumference of the wheel, calculated by $C = \pi d$. Substitute $\pi = \frac{22}{7}$ and $d = \frac{5}{4}\text{ ft}$:
$$C = \frac{22}{7} \times \frac{5}{4} = \frac{110}{28} = \frac{55}{14} \approx 3.93\text{ ft}$$

Step2: Calculate total travel distance

Multiply the circumference by the number of revolutions (254):
$$\text{Total Distance} = \frac{55}{14} \times 254 = \frac{55 \times 254}{14} = \frac{13970}{14} = \frac{6985}{7} \approx 997.86\text{ ft}$$

Answer:

A. The wheel rolls $\frac{55}{14}$ feet (or approximately 3.93 feet) for one revolution.
B. The total distance recorded is $\frac{6985}{7}$ feet (or approximately 997.86 feet).