Question

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

Answer 1

32.84 I just took the test

Answer 2

Answer:

The arc length is $32.84\ cm$    

Step-by-step explanation:

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=36\frac{3}{5}\ cm=\frac{36*5+3}{5}=\frac{183}{5}\ cm$

substitute

$C=2(3.14)(\frac{183}{5})=229.848\ cm$

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

$\frac{229.848}{2\pi}=\frac{x}{2\pi/7}\\ \\x=229.848*(2\pi/7)/(2\pi)\\ \\x=`32.84\ cm$