Question

In a circle with a radius of 36 3/5 cm, an arc is intercepted by a central angle of 2π7 radians.

What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.


cm

Answer 1

32.84 I just took the test

Answer 2

The arc length is
`32.84\ cm`

Explanation:

we know that

The circumference of a circle is equal to

`C=2\pi r`

we have

`r=36(3)/(5)\ cm=(36*5+3)/(5)=(183)/(5)\ cm`

substitute

`C=2(3.14)((183)/(5))=229.848\ cm`

Remember that

`2\pi` radians subtends the complete circle of length
`229.848\ cm`

so

by proportion

Find the arc length by a central angle of
`2\pi/7` radians

`(229.848)/(2\pi)=(x)/(2\pi/7)\\ \\x=229.848*(2\pi/7)/(2\pi)\\ \\x=`32.84\ cm`