To find the length of the arc of a circle corresponding to a central angle, you can use the formula:
\[ \text{Length of arc} = \frac{\theta}{360^\circ} \times 2\pi r \]
where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.
In your case:
- The radius \(r = 10\) cm,
- The central angle \(\theta = 70^\circ\).
Now, substituting these values into the formula:
\[ \text{Length of arc} = \frac{70}{360} \times 2\pi \times 10 \]
Calculating this step-by-step:
-
Calculate \(2\pi \times 10\): \[ 2\pi \times 10 \approx 62.83 \text{ cm} \]
-
Calculate the fraction: \[ \frac{70}{360} = \frac{7}{36} \approx 0.1944 \]
-
Now multiply: \[ \text{Length of arc} \approx 0.1944 \times 62.83 \approx 12.2 \text{ cm} \]
Thus, the length of the arc subtended by a central angle of 70 degrees in a circle with a radius of 10 cm is approximately 12.2 cm.
1 answer