R=10cm angle is 70, what is length of arc

1 answer

To find the length of an arc of a circle, you can use the formula:

\[ \text{Arc Length} = \frac{\theta}{360} \times 2\pi R \]

where:

  • \(\theta\) is the angle in degrees,
  • \(R\) is the radius of the circle.

In your case, \(R = 10\) cm and \(\theta = 70\) degrees.

Plugging in the values:

\[ \text{Arc Length} = \frac{70}{360} \times 2\pi \times 10 \]

Calculating this step by step:

  1. Calculate \(2\pi \times 10\): \[ 2\pi \times 10 \approx 62.83 \text{ cm} \]

  2. Find the fraction of the circle represented by the angle: \[ \frac{70}{360} \approx 0.1944 \]

  3. Multiply the fraction by the circumference: \[ \text{Arc Length} \approx 0.1944 \times 62.83 \approx 12.2 \text{ cm} \]

Therefore, the length of the arc is approximately 12.2 cm.