The area of shaded sector is [tex]\boxed{11.45{\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 diameter of the circle is [tex]5.4{\text{ cm}}.[/tex]
The central angle is [tex]{180^ \circ }.[/tex]
The given options are as follows,
(A). [tex]11.45{\text{ c}}{{\text{m}}^2}[/tex]
(B). [tex]16.96{\text{ c}}{{\text{m}}^2}[/tex]
(C). [tex]22.90{\text{ c}}{{\text{m}}^2}[/tex]
(D).[tex]8.48{\text{ c}}{{\text{m}}^2}[/tex]
Explanation:
The diameter of the sector is [tex]5.4{\text{ cm}}[/tex] and the angle is [tex]\theta = {180^ \circ }.[/tex]
The radius of the circle can be calculated as follows,
[tex]\begin{aligned}{\text{Radius}}&=\frac{{{\text{Diameter}}}}{{\text{2}}}\\&=\frac{{5.4}}{2}\\&= 2.7\\\end{aligned}[/tex]
The radius of the circle is [tex]2.7{\text{ cm}}.[/tex]
The area of shaded sector can be calculated as follows,
[tex]\begin{aligned}{\text{Area of sector}} &= \frac{\theta }{{360}} \times \pi {r^2}\\&=\frac{{180}}{{360}} \times \frac{{22}}{7} \times {\left( {2.7} \right)^2}\\&= \frac{1}{2} \times \frac{{22}}{7} \times \left( {7.29} \right)\\&= \frac{{160.38}}{{14}}\\&= 11.45{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
The area of shaded sector is [tex]\boxed{11.45{\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, arc length, radian, central angle, intercepted, circle, circumference, sector of a circle, minor sector, major sector, segment, angle.
