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2 months ago

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

Mathematics

2 answers:

PIT_PIT [12.4K]2 months ago

8 0

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

zzz [12.3K]2 months ago

4 0

The shaded sector's area is $\boxed{26.5{\text{ c}}{{\text{m}}^2}}.$ Option (A) is the right answer.

Additional explanation:

The area of a sector can be calculated using the formula provided below,

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

Here, $\theta$ indicates the central angle and r represents the circle's radius.

Details provided:

The radius is $4.5{\text{ cm}}.$

and the central angle is ${150^ \circ }.$

The options available include:

(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 is $4.5{\text{ cm}}$ and the central angle is $\theta = {150^ \circ }.$

The area for the shaded sector can be derived 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 the shaded sector equals $\boxed{26.5{\text{ c}}{{\text{m}}^2}}$ . Therefore, Option (A) is the correct answer.

The correct answer is Option (A).

Option (B) is not the right answer.

Option (C) is not accurate.

Option (D) is incorrect.

Additional resources:

1.Read more about the function's inversehttps://[[TAG_91]][[TAG_92]].[[TAG_93]][[TAG_94]][[TAG_95]]2.[[TAG_96]] Read about circle equations .

3.Learn more about the function's range and domain

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.

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