Question

if the sector of a circle with radius 10 cm with central angle is 18° then find the area of the sector (π=3.14)​

Answer 1

Radius of the circle = 10cm

Central angle is 18°

Area of sector =

$area \: ofsector = \frac{x}{360} \times \pi \times r {}^{2}$

=

$\frac{18}{360} \times 3.14 \times 100$

=78.57

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Answer 2

✰Answer✰

☛Given:

• Radius= 10cm
• Central angle of sector=18°

☛To find:

• Area of the sector.

✰Formula used✰

☛Area of sector

$\large{ \sf{ \boxed{ = \frac{ \theta \: }{360} \times \pi {r}^{2} }}}$

☛By using formula,

$\large{ \sf{ = \frac{18}{360} \times 3.14 \times {10}^{2} }} \: \: cm {}^{2} \\ \\ \large{ \sf{ = \cancel{ \frac{18}{360 \: \: \: \cancel{ 20}}} \times 3.14 \times \cancel{ 100} \: \: 5}} \: {cm}^{2} \\ \\ \large{ \sf{ = 3.14 \times 5 \: }} \: {cm}^{2} \\ \\ \large{ \sf{ \boxed{ \purple{ = 15.70 \: {cm}^{2} }}}}$

✰So Final Answer✰

$\large{ \boxed{ \red{ \sf{area \: of \: sector = 15.70 \: {cm}^{2} }}}}$

✰Related Concept✰

$\large{ \sf{ \underline{ \green{sector \: of \: circle}}}}$

☛A sector is a part of circle formed by an arc and two radiis. A shape of a sector can be compared with a slice of pie or pizza.

☛A sector divides the circle into two regions known as Major sector and Minor sector.

☛In a circle with radius and centre O , Let a sector is there with angle theta. Then we can find the area of sector by unitary method.

$\large{ \sf{ \rightarrow \: we \: know \: area \: of \: circle = \pi {r}^{2} }} \\ \\ \large{ \sf{we \: can \: say \: it \: is \: a \: sector \: of \:angle 360}} \\ \\ \large{ \sf{ \rightarrow \: when \: the \: angle \: is \: 1 \: then \: area \: of \: sector}} \\ \\ \large{ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi {r}^{2} }{360} }} \\ \\ \large{ \sf{ \rightarrow \: if \: angle \: would \: be \: \theta \: then \: area \: of \: sector}} \\ \\ \large{ \sf{ \boxed{ \red{ = \frac{ \theta}{360} \times \pi {r}^{2} }}}} \\ \\ \large{ \sf{ \therefore{required \: formula}}}$