Question

$\huge\bigstar\underline\mathfrak{Question\;For\;brainly:-}$

Find the area of sector of a circle with radius 14 cm if angle of the sector is 90°​

Answer 1

Given:-

• Radius of the Circle = 14 cm
• Sector angle = 90°

To find:-

• Area of the sector

Diagram:-

$\setlength{\unitlength}{1.2mm}\begin{picture}(50,55)\thicklines\qbezier(25.000,10.000)(33.284,10.000)(39.142,15.858)\qbezier(39.142,15.858)(45.000,21.716)(45.000,30.000)\qbezier(45.000,30.000)(45.000,38.284)(39.142,44.142)\qbezier(39.142,44.142)(33.284,50.000)(25.000,50.000)\qbezier(25.000,50.000)(16.716,50.000)(10.858,44.142)\qbezier(10.858,44.142)( 5.000,38.284)( 5.000,30.000)\qbezier( 5.000,30.000)( 5.000,21.716)(10.858,15.858)\qbezier(10.858,15.858)(16.716,10.000)(25.000,10.000)\put(25,30){\line(5,0){20}}\put(25,30){\circle*{1}}\put(30,32){\sf\large{14 cm}}\put(25,30){\line(0, - 5){20}}\put(16,20){\sf\large{14 cm}}\put(28,30){\line(0, - 5){3}}\put(25,27){\line(5,0){3}}\put(30,25){\sf\large{ \sf 90^\circ }}\end{picture}$

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Solution:-

We know that,

$\star\;{\boxed{\sf{\purple{Area_{\;(sector)} = \dfrac{ \theta}{360^\circ} \times \pi r^2}}}}$

Now, Putting given values in formula,

$:\implies\sf { \dfrac{90^\circ}{360^\circ}} \times \dfrac{22}{ \cancel{7}} \times \cancel{14} \times 14$

$:\implies\sf \frac{1}{4} \times 44 \times 14$

$:\implies\sf 11 \times 14$

$:\implies{\boxed{\frak{\pink{154\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\;sector\;is\; \bf{154\;cm^2}.}}}$

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Answer 2

Answer:

Given:

• Radius of the circle = 14cm

• Angle of the sector = 90° .

To find:

• Area of the sector = ?.

Solution:

• As we know that:

\begin{gathered} \star \boxed{ \red{\bold{ area \: of \: sector \: = \frac{ \theta}{360 \degree} \times \pi {r}^{2} }}} \\ \end{gathered}

⋆

areaofsector=

360°

θ

×πr

2

• put the given values :

\begin{gathered} \implies \: area \: of \: sector = \frac{90 \degree}{360 \degree} \times \frac{22}{7} ({14}^{2} ) \\ \\ \implies \: area \: of \: sector = \frac{1}{4} \times 44 \times 14 \\ \\ \implies \: area \: of \: sector = 11 \times 14 \\ \\ \implies \: area \: of \: sector = 154 {cm}^{2} \end{gathered}

⟹areaofsector=

360°

90°

×

7

22

(14

2

)

⟹areaofsector=

4

1

×44×14

⟹areaofsector=11×14

⟹areaofsector=154cm

2

Hence, The area of the sector is 154cm².

Step-by-step explanation:

Hope it will help you..