jogalloway30
contestada

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

Respuesta :

larsonjoseph01
32.84 I just took the test
calculista

Answer:

The arc length is [tex]32.84\ cm[/tex]    

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=36\frac{3}{5}\ cm=\frac{36*5+3}{5}=\frac{183}{5}\ cm[/tex]

substitute

[tex]C=2(3.14)(\frac{183}{5})=229.848\ cm[/tex]

Remember that

[tex]2\pi[/tex] radians subtends the complete circle of length [tex]229.848\ cm[/tex]

so

by proportion

Find the arc length by a central angle of [tex]2\pi/7[/tex] radians

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

Otras preguntas