(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 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.
