High School

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How many times does a wheel with a radius of 14 cm rotate to cover a distance of 176 m?

(Use [tex]$\pi = \frac{22}{7}$[/tex])

Answer :

We are given a wheel with a radius of [tex]$14$[/tex] cm and asked to find how many rotations it makes over a distance of [tex]$176$[/tex] m. Follow these steps:

1. Convert the distance into centimeters since the radius is given in centimeters:
[tex]$$
\text{Distance} = 176 \text{ m} \times 100 = 17600 \text{ cm}.
$$[/tex]

2. Calculate the circumference of the wheel. The formula for the circumference is:
[tex]$$
C = 2\pi r.
$$[/tex]
Here, [tex]$r = 14$[/tex] cm and we are using [tex]$\pi = \frac{22}{7}$[/tex]. Substitute these values:
[tex]$$
C = 2 \times \frac{22}{7} \times 14.
$$[/tex]
Simplify the expression:
[tex]$$
C = 2 \times \frac{22 \times 14}{7} = 2 \times 44 = 88 \text{ cm}.
$$[/tex]

3. Determine the number of rotations by dividing the total distance by the circumference:
[tex]$$
\text{Rotations} = \frac{\text{Total Distance}}{C} = \frac{17600}{88} = 200.
$$[/tex]

Thus, the wheel rotates [tex]$\boxed{200}$[/tex] times to cover a distance of [tex]$176$[/tex] m.

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