Respuesta :
[tex]\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=4.5\\
\theta =150
\end{cases}\implies A=\cfrac{(150)(\pi )(4.5)^2}{360}\\\\\\ A=\cfrac{3037.5\pi }{360}[/tex]
The area of shaded sector is [tex]\boxed{26.5{\text{ c}}{{\text{m}}^2}}.[/tex] Option (A) is correct.
Further explanation:
The formula for area of sector can be expressed as follows,
[tex]\boxed{{\text{Area of sector}} = \frac{\theta }{{{{360}^ \circ }}} \times \pi {r^2}}[/tex]
Here, [tex]\theta[/tex] is the central angle and r is the radius of the circle.
Given:
The radius of the circle is [tex]4.5{\text{ cm}}.[/tex]
The central angle is [tex]{150^ \circ }.[/tex]
The given options are as follows,
(A). [tex]26.5{\text{ c}}{{\text{m}}^2}[/tex]
(B). [tex]11.78{\text{ c}}{{\text{m}}^2}[/tex]
(C).[tex]53.0{\text{ c}}{{\text{m}}^2}[/tex]
(D). [tex]5.89{\text{ c}}{{\text{m}}^2}[/tex]
Explanation:
The radius of the sector is [tex]4.5{\text{ cm}}[/tex] and the central angle is [tex]\theta = {150^ \circ }.[/tex]
The area of shaded sector can be obatined as follows,
[tex]\begin{aligned}{\text{Area of sector}} &= \frac{\theta }{{360}} \times \pi {r^2}\\&=\frac{{150}}{{360}} \times \frac{{22}}{7} \times {\left( {4.5} \right)^2}\\&= \frac{5}{{12}} \times \frac{{22}}{7} \times \left( {20.25}\right)\\&= \frac{{2227.5}}{{84}}\\&= 26.5{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
The area of shaded sector is [tex]\boxed{26.5{\text{ c}}{{\text{m}}^2}}[/tex]. Option (A) is correct.
Option (A) is correct.
Option (B) is not correct.
Option (C) is not correct.
Option (D) is not correct.
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: Area of Circles
Keywords: Radius of circle, area of shaded region, arc length, radian, central angle, intercepted, circle, circumference, sector of a circle, minor sector, major sector, segment, angle.
