Sure, let's solve this step-by-step:
1. Convert the radius from centimeters to meters:
The radius of the wheel is given as 28 cm. To convert this to meters, we divide by 100 (since 1 meter = 100 centimeters).
[tex]\[
\text{Radius in meters} = \frac{28 \text{ cm}}{100} = 0.28 \text{ meters}
\][/tex]
2. Calculate the circumference of the wheel:
The circumference [tex]\(C\)[/tex] of the wheel can be found using the formula for the circumference of a circle, [tex]\(C = 2 \pi r\)[/tex], where [tex]\(r\)[/tex] is the radius and [tex]\(\pi\)[/tex] is approximately [tex]\( \frac{22}{7} \)[/tex].
[tex]\[
C = 2 \times \frac{22}{7} \times 0.28
\][/tex]
Simplifying this:
[tex]\[
C = 2 \times \frac{22}{7} \times 0.28 = 2 \times 3.142857 \times 0.28 \approx 1.76 \text{ meters}
\][/tex]
3. Calculate the number of rotations:
To find out how many rotations the wheel needs to cover a distance of 8.8 meters, we divide the total distance by the circumference of the wheel.
[tex]\[
\text{Number of rotations} = \frac{\text{Distance}}{\text{Circumference}} = \frac{8.8 \text{ meters}}{1.76 \text{ meters}} = 5
\][/tex]
Therefore, to cover a distance of 8.8 meters, the wheel must make:
[tex]\[
\boxed{5}
\][/tex]
rotations. Hence, the correct option is (2) 5.
