Question

What is the radius of a circle in which a 30° arc is 2

inches long?
24 inches
O 12 inches
o 213 inches

Answer 1

The radius of the circle is 12 inches.

Explanation:

Given:

The radius of a circle in which a 30° arc is 2π.

Now, we put the formula of circumference first.

`C=2\pi r`

Now, since 30 is one twelfth of 360, a 30° arc will be one twelfth of the whole circumference. So, if you call the arc length A, you have:

`A=(C)/(12)=(2\pi r)/(12)=(\pi r)/(6)`

So, we know the arc length, now we can put the value and solve the following equation:

`(\pi r)/(6)=2\pi`

Multiplying both sides by 6 and then dividing both sides by π we get :

`r=12`.

Therefore, the radius of the circle is 12 inches.