Question

What is the approximate area of the shaded sector in the circle shown below

Answer 1

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=4.5\\ \theta =150 \end{cases}\implies A=\cfrac{(150)(\pi )(4.5)^2}{360}\\\\\\ A=\cfrac{3037.5\pi }{360}$

Answer 2

The area of shaded sector is $\boxed{26.5{\text{ c}}{{\text{m}}^2}}.$ Option (A) is correct.

Further explanation:

The formula for area of sector can be expressed as follows,

$\boxed{{\text{Area of sector}} = \frac{\theta }{{{{360}^ \circ }}} \times \pi {r^2}}$

Here, $\theta$ is the central angle and r is the radius of the circle.

Given:

The radius of the circle is $4.5{\text{ cm}}.$

The central angle is ${150^ \circ }.$

The given options are as follows,

(A). $26.5{\text{ c}}{{\text{m}}^2}$

(B). $11.78{\text{ c}}{{\text{m}}^2}$

(C).$53.0{\text{ c}}{{\text{m}}^2}$

(D). $5.89{\text{ c}}{{\text{m}}^2}$

Explanation:

The radius of the sector is $4.5{\text{ cm}}$ and the central angle is $\theta = {150^ \circ }.$

The area of shaded sector can be obatined as follows,

$\begin{aligned}{\text{Area of sector}} &= \frac{\theta }{{360}} \times \pi {r^2}\\&=\frac{{150}}{{360}} \times \frac{{22}}{7} \times {\left( {4.5} \right)^2}\\&= \frac{5}{{12}} \times \frac{{22}}{7} \times \left( {20.25}\right)\\&= \frac{{2227.5}}{{84}}\\&= 26.5{\text{ c}}{{\text{m}}^2}\\\end{aligned}$

The area of shaded sector is $\boxed{26.5{\text{ c}}{{\text{m}}^2}}$. 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 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.