Question

If the radius of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

a.3 7 ? inches

b.7 2 ? inches

c.7 3 ? inches

d.7 6 ? inches

Answer 1

`L = \cfrac{ \pi rn}{180} \ \ \ \ \ \ \ [\text{L=arc length, r=radius, n=central angle,} \ \pi \approx3.14 ] \\ \\ \\ L = \cfrac{ 3.14*6*70}{180} \approx7.33 \ in`

Answer 2

Option C.
`(7)/(3)\pi \ in`

Explanation:

we know that

The circumference of a circle is equal to

`C=2\pi r`

In this problem we have

`r=6\ in`

substitute

`C=2\pi (6)=12\pi\ in`

Remember that

`360\°` subtends the complete arc of length
`12\pi\ in`

so

by proportion

Find the arc length by an angle measuring
`70\°`

`(360)/(12\pi )=(70)/(x)\\ \\x=12\pi *70/360\\ \\x=(840)/(360)\pi \\ \\x=(7)/(3)\pi \ in`