Arc of circle radius is 10cm substended by angle of 70 degrees

1 answer

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:

  1. Calculate \( \frac{70}{360} \): \[ \frac{70}{360} = \frac{7}{36} \approx 0.1944 \]

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

  3. 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.