The radius of a circle is 6 meters. What is the length of a 135° arc?

Question

i do not know this question i need help -- The radius of a circle is 6 meters. What is the length of a 135° arc?

Answer 1

The total circumference of the circle is:

 

C = 2*pi*radius = 2*(3.14159)*(6) = 37.7 m

 

The total circle has 365^o.  Your arc has only 135^o.  Hence:

 

135^o           x

-------  =  -------------

365^o          37.7 m

 

where x is the length of the 135^o arc.  Solve for x.

Answer 2

Remember two things:

 

- There are 360° in a circle. which is the same as saying that a circle is an arc of 360°

- The circumference of a circle is 2π times the radius.  And the circumference is the same as the length of an arc that goes all the way around the circle, or a 360° arc. 

 

So from this you can figure out the length of any arc, as long as you know the radius, because...

 

If θ is the number of degrees in the arc, then θ / 360 is the fraction of the circle that the arc takes up.  So multiply this fraction by the total circumference (2πr), to get the length of the arc.

 

That gives you a general formula:

 

L = 2πrθ / 360

 

In this case, r = 6 and θ = 135°.  So...

 

L = 2π * 6 * 135 / 360 = 4.5 π

 

 

Answer 3

Let

 

 s: arc length

 r: radius of circle

 θ: angle measurement

 

The formula for arc length is    s=rθ

 

Hence, s=(6)(135)=810 meters