for the sector with given measures find the length of the arc, area annd perimeter (π=3.14) , ii) central angle = 120° ,ø =120
Answers
Answer:
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Step-by-step explanation:
Length is 13.2 cm , Area is 41.5 cm² and Perimeter is 25.8 cm
Step-by-step explanation:
Given:
Central angle of sector, \thetaθ = 120°
Diameter of the circle = 12.6 cm
⇒ radius of the circle, r = 6.3 cm
Value of π = 3.14
To find: Length of the arc of the sector, Area of the sector and perimeter of the sector.
Formula we use are as follows,
Length\:of\:arc=\frac{\theta}{360^{\circ}}\times2\pi rLengthofarc=
360
∘
θ
×2πr
Area\:of\:the\:Sector=\frac{\theta}{360^{\circ}}\times\pi r^2AreaoftheSector=
360
∘
θ
×πr
2
Perimeter of the sector = Length of arc + 2 × radius
So,
Length\:of\:arc=\frac{120}{360}\times2(3.14)(6.3)=13.188=13.2\:cmLengthofarc=
360
120
×2(3.14)(6.3)=13.188=13.2cm
Area\:of\:the\:Sector=\frac{120}{360}\times3.14(6.3)^2=41.5422=41.5\:cm^2AreaoftheSector=
360
120
×3.14(6.3)
2
=41.5422=41.5cm
2
Perimeter of the sector = 13.2 + 2 × 6.3 = 25.8 cm
Therefore, Length is 13.2 cm , Area is 41.5 cm² and Perimeter is 25.8 cm