Radius of circle is 10cm substended by central angle of 70, why is the length of circle

1 answer

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:

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

  2. Calculate the fraction: \[ \frac{70}{360} = \frac{7}{36} \approx 0.1944 \]

  3. 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.