To find the length of an arc of a circle, you can use the formula:
\[ L = \frac{\theta}{360} \times 2\pi r \]
where:
- \( L \) is the length of the arc,
- \( \theta \) is the central angle in degrees,
- \( r \) is the radius of the circle.
In your case, the radius \( r = 10 , \text{cm} \) and the angle \( \theta = 70^\circ \).
Now plug the values into the formula:
\[ L = \frac{70}{360} \times 2\pi \times 10 \]
Calculating step-by-step:
-
Calculate \( \frac{70}{360} \): \[ \frac{70}{360} = \frac{7}{36} \approx 0.1944 \]
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Calculate \( 2\pi \times 10 \): \[ 2\pi \times 10 \approx 62.83 , \text{cm} \]
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Multiply by \( \frac{7}{36} \): \[ L \approx 0.1944 \times 62.83 \approx 12.19 , \text{cm} \]
Thus, the length of the arc is approximately 12.19 cm.