 # For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with o length of 7 3 π meters? 140

Step-by-step explanation:

If it is an arc of 7pi/3, and the circumference is 6*pi or 6pi, then the arc takes up 7/18 of the circle, and since a circle has 360 degrees, the answr is 7/18 * 360 or 140. ..............................   Step-by-step explanation:

We know that, where,

θ = central angle in radian.

Given,

diameter = 6 m, so radius = 3 m. Putting the values,    Answer : The measurement of a central angle is, Step-by-step explanation :

Formula used for angle subtended by an arc is: where,

s = arc length = r = radius = Now put all the given values in the above formula, we get:   Thus, the measurement of a central angle is,  Step-by-step explanation: The measurement of a central angle (in degrees) subtended by an arc is .

Step-by-step explanation:

as meters

so meters

and meters

Using the formula        Simplify   Therefore, the measurement of a central angle (in degrees) subtended by an arc is . The measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

Step-by-step explanation:

Here, the diameter of the circle = 6 m

So, radius  = D / 2  = 6 / 2  = 3 m

Also, the length of the arc = ( ) meters

Putting π  = 3.14, we get

The length S of the arc = or, S  = 7.85 m

Let us assume the arc subtends angle Ф at the center of the circle.

⇒  S  = r Ф

or, Ф = Now, 1 Radian  = 57.2958 Degrees

⇒ 2. 62 Radian  = 2.61  x  ( 57.2958 Degrees)  =  149.542 °

or, Ф    =  149.542°

Hence, the measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542° Arc length = (5/2) * PI meters = 7.853981634 meters
circle circumference = 2 * PI * radius = 2 *PI * 3
18.8495559215
arc length = (7.85381634 / 18.8495559215) * 360 =
0.4166578975 *360 =
150 degrees Arc length is given by:
C=θ/360πd
thus plugging in the values we get:
5/2π=θ/360π*6
dividing through by 6π we get:
5/12=θ/360
multiplying both sides by 360
θ=150° Arc length=5/2 pi
diameter=6m
Circumference=pi x d=pi x 6m= 6pi

Circumference/arc length=6pi/(5/2pie)=360degree/central angle

6pie x central angle=360degree x 5/2pie

Central angle=360degree x 5/2pie/6pie

Central angle=360degree x 5/12

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