To find the circumference (length) of the entire circle when given the length of an arc and the central angle that subtends it, you can use the following relationship:
The length of the arc \( L \) is given by the formula:
\[ L = \frac{\theta}{360} \times C \]
where:
- \( L \) is the length of the arc,
- \( \theta \) is the central angle in degrees,
- \( C \) is the circumference of the circle.
In this case, you are given:
- \( L = 10 , \text{cm} \)
- \( \theta = 70^\circ \)
Now, rearranging the formula to solve for the circumference \( C \):
\[ C = \frac{L \times 360}{\theta} \]
Substituting the known values:
\[ C = \frac{10 \times 360}{70} \]
Now, calculate \( C \):
\[ C = \frac{3600}{70} = 51.43 , \text{cm} \]
Thus, the circumference of the circle is approximately \( 51.43 , \text{cm} \).