Question

derive and apply formulas for circumference
homework
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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?

1. use structure hans opens a circular window

that is 3.5 feet across at its widest point. what is the
circumference of the window to the nearest whole
number? use 3.14 for $pi$.
diameter $\frac{5}{4}$ ft

Explanation:

Step1: Find 1 revolution distance (A)

The distance for one revolution is the wheel's circumference, calculated by $C = \pi d$.
$C = \frac{22}{7} \times \frac{5}{4}$
$C = \frac{110}{28} = \frac{55}{14} = 3\frac{13}{14}$ ft

Step2: Find total distance (B)

Multiply 1 revolution distance by total revolutions.
$\text{Total Distance} = \frac{55}{14} \times 254$
$\text{Total Distance} = \frac{55 \times 254}{14} = \frac{13970}{14} = 997\frac{12}{14} = 997\frac{6}{7}$ ft

Step3: Find window circumference

Use $C = \pi d$, with $d=3.5$ ft, $\pi=3.14$.
$C = 3.14 \times 3.5$
$C = 10.99 \approx 11$ ft

Answer:

1. A. $3\frac{13}{14}$ feet

B. $997\frac{6}{7}$ feet

1. 11 feet