Question

The following sector has a radius of 10 inches and a central angle of 30 . Which of the following is its arc length, in inches?

Answer 1

option 1

Explanation:

step 1

Find the arc length of the complete circle

The circumference of the circle ios given by

`C=2\pi r`

we have

`r=10\ in`

substitute

`C=2\pi (10)`

`C=20\pi\ in`

step 2

Find the arc length for a sector with a cenytral angle of 30 degrees

we know that

The complete circle subtends a central angle of 360 degrees

so

using proportion

`(20\pi)/(360^0)=(x)/(30^o)\\\\x=20\pi(30)/360\\\\x=(5)/(3) \pi\ in`