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

Answer:

option 1

Step-by-step 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

$\frac{20\pi}{360^0}=\frac{x}{30^o}\\\\x=20\pi(30)/360\\\\x=\frac{5}{3} \pi\ in$