Question

Example 2 : Find the area of the sector of a circle
with radius 4 cm and of angle 30°. Also, find the area
of the corresponding major sector (Use = 3.14).​

Answer 1

Answer:

I hope this is ur req answer..

Answer 2

$\sf Here \begin{cases} & \sf{ \theta = 30^\circ } \\ & \sf{Radius,\; r = 4\;cm} \end{cases}$

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Therefore,

Area of sector OAPB,

$\qquad\quad\sf \dfrac{ \theta}{360} \times \pi r^2$

$:\implies\sf \dfrac{30}{360} \times 3.14 \times 4 \times 4$

$:\implies\sf \dfrac{3.14 \times 4}{3}$

$:\implies{\underline{\boxed{\sf{\pink{4.153\;cm^2}}}}}\;\bigstar$

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☯ Let A be the area of corresponding major sector. Then,

A = Area of sector OAQB

A = Area of circle - Area of corresponding minor sector

$:\implies\sf A = \pi r^2 - \dfrac{ \theta}{360} \times \pi r^2$

$:\implies\sf A = \pi r^2 \bigg\lgroup\sf 1 - \dfrac{ \theta}{360}\bigg\rgroup$

$:\implies\sf A = 3.14 \times 4 \times 4 \bigg\lgroup\sf 1 - \dfrac{30}{360}\bigg\rgroup$

$:\implies\sf A = 3.14 \times 4 \times 4 \times \cancel{ \dfrac{330}{360}}$

$:\implies\sf A = 3.14 \times 4 \times 4 \times \dfrac{11}{12}$

$:\implies\sf A = \dfrac{3.14 \times 44}{3}$

$:\implies{\underline{\boxed{\sf{\purple{A = 46.05\;cm^2}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Area\;of\;Major\;sector\;is\; \bf{46.05\;cm^2}.}}}$