Question

What is the circumference of the circle shown below, given that the length of

Answer 1

Given:

Length of arc AB is 4 units.

The measure of central angle corresponding to arc AB is 30 degrees.

To find:

The circumference of the circle.

Solution:

The formula for arc length is:

$s=2\pi r\dfrac{\theta }{360^\circ}$

Where, r is the radius and $\theta$ is the central angle.

It is also written as:

$s=C\dfrac{\theta }{360^\circ}$

Where, C is the circumference of the circle.

Putting $s=4,\theta =30^\circ$ in the above formula, we get

$4=C\dfrac{30^\circ}{360^\circ}$

$4=\dfrac{1}{12}C$

Multiply both sides by 12.

$4\times 12=C$

$48=C$

The circumference of the circle is 48 units.

Therefore, the correct option is A.