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

1 answer

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 \( 51.43 , \text{cm} \).