Question

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

Answer 1

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