Question

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?

Answer 1

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 2

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

(2). The length of the arc of a circle is $\boxed{152.04}.$

Further explanation:

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

$\boxed{\theta=\dfrac{l}{r}}.$

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 $\dfrac{{9\pi }}{5}.$

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,

$\begin{aligned}\theta&= \frac{{5.4}}{6}\\&= 0.9{\text{ radian}}\\\end{aligned}$

The central angle of a circle is $\boxed{0.9{\text{ radian}}}.$

(2)

The radius of the circle is 56.9 m and the central angle is $\dfrac{{9\pi }}{5}$

The length of an arc can be calculated as follows,

$\begin{aligned}\frac{{9\pi }}{5}&= \frac{l}{{26.9}}\\\frac{{9 \times 3.14}}{5}&= \frac{l}{{26.9}}\\\frac{{28.26}}{5}\times 26.9 &= l\\152.04&= l\\\end{aligned}$

The length of the arc of a circle is $\boxed{152.04}.$

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 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.