To determine the length of the arc intersected by a central angle of [tex]\(\frac{\pi}{2}\)[/tex] radians in a circle with a radius of 4.5 cm, follow these steps:
1. Identify the given values:
- Radius ([tex]\(r\)[/tex]) of the circle: 4.5 cm
- Central angle ([tex]\(\theta\)[/tex]) in radians: [tex]\(\frac{\pi}{2}\)[/tex]
2. Use the formula for arc length:
The arc length ([tex]\(L\)[/tex]) of a circle is given by the formula:
[tex]\[
L = r \times \theta
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
L = 4.5 \, \text{cm} \times \frac{\pi}{2}
\][/tex]
4. Use the approximation [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[
\frac{\pi}{2} \approx \frac{3.14}{2} = 1.57
\][/tex]
Thus,
[tex]\[
L = 4.5 \, \text{cm} \times 1.57
\][/tex]
5. Calculate the arc length:
[tex]\[
L = 4.5 \times 1.57 = 7.065 \, \text{cm}
\][/tex]
6. Round the arc length to the nearest tenth:
[tex]\[
L \approx 7.1 \, \text{cm}
\][/tex]
The length of the arc is approximately 7.1 cm.
