Question

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

Answer 1

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**.