Wheel Radius Calculation
The problem asks for the radius of a wheel given the number of revolutions it makes and the total distance covered. We need to find the radius in meters.
Distance Conversion
First, convert the total distance from kilometers (km) to meters (m):
Distance = $154 \text{ km} = 154 \times 1000 \text{ m} = 154000 \text{ m}$
Circumference Calculation
The distance covered in one revolution is equal to the circumference of the wheel.
Total revolutions = $1000$
Distance per revolution (Circumference) = Total Distance / Total Revolutions
Circumference = $\frac{154000 \text{ m}}{1000} = 154 \text{ m}$
Radius Determination
The formula for the circumference ($C$) of a circle (wheel) with radius ($r$) is $C = 2 \pi r$.
We know the circumference is $154$ m. We can use the value of $\pi \approx \frac{22}{7}$.
$154 = 2 \times \frac{22}{7} \times r$
$154 = \frac{44}{7} \times r$
To find the radius ($r$), rearrange the formula:
$r = 154 \div \frac{44}{7}$
$r = 154 \times \frac{7}{44}$
Simplify the calculation:
$r = \frac{154}{44} \times 7$
$r = \frac{14 \times 11}{4 \times 11} \times 7$
$r = \frac{14}{4} \times 7$
$r = \frac{7}{2} \times 7$
$r = \frac{49}{2}$
$r = 24.5 \text{ m}$
Final Answer Format
Convert the radius to a mixed fraction:
$r = 24.5 \text{ m} = 24 \frac{1}{2} \text{ m}$
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