1. What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercept arc length is 5.4 cm?

Make sure to show all calculations.

2. In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π59π5 radians.

What is the arc length?

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

Make sure to show your calculations

1.
find circumferece
c=2pir
c=2*6*pi=12pi
intercept is 5.4

2pi radians=all

part/whole=part/whole
5.4/12pi=x/2pi
times both sides by 12pi
5.4=6x
divide both sides by 6
0.9=x
answer is 0.9 radians

2.
assuming 9pi/5 radians

find circumference
c=2pir
c=2*26.9*pi
c=53.8pi

arc/circumference=(9pi/5)/2pi

x/(53.8pi)=(9pi/5)/(2pi)
x/(53.8pi)=18/5
times both sides by 53.8pi
x=608.46266 m
about x=608.46 m

Answer Link

AkshayG AkshayG · Answer 2 · 2019-10-20T21:01:06+02:00

(1). The measure in radians for the central angle of a circle with radius 6 cm and arc length 5.4 cm is [tex]\boxed{0.9{\text{ radian}}}.[/tex]

(2). The length of the arc of a circle is [tex]\boxed{152.04}.[/tex]

Further explanation:

The relationship between the length of arc “l”, radius of circle “r” and the central angle “[tex]\theta[/tex]” can be expressed as follows,

[tex]\boxed{\theta=\dfrac{l}{r}}.[/tex]

Given:

(1). The radius of a circle is 6 cm and the intercept arc length is 5.4 cm.

(2). The radius of the circle is 56.9 m and the central angle is [tex]\dfrac{{9\pi }}{5}.[/tex]

Explanation:

(1)

The radius of the circle is 6 cm and the intercept arc length is 5.4 cm.

Central angle of a circle can be calculated as follows,

[tex]\begin{aligned}\theta&= \frac{{5.4}}{6}\\&= 0.9{\text{ radian}}\\\end{aligned}[/tex]

The central angle of a circle is [tex]\boxed{0.9{\text{ radian}}}.[/tex]

(2)

The radius of the circle is 56.9 m and the central angle is [tex]\dfrac{{9\pi }}{5}[/tex]

The length of an arc can be calculated as follows,

[tex]\begin{aligned}\frac{{9\pi }}{5}&= \frac{l}{{26.9}}\\\frac{{9 \times 3.14}}{5}&= \frac{l}{{26.9}}\\\frac{{28.26}}{5}\times 26.9 &= l\\152.04&= l\\\end{aligned}[/tex]

The length of the arc of a circle is [tex]\boxed{152.04}.[/tex]

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Circles

Keywords: Radius of circle, arc length, radian, central angle, intercepted, circle, circumference, sector of a circle.