Question

The area of a sector of a circle of radius 2 cm is π cm². Find the angle contained by the sector.

Answer 1

Answer:

The angle contained by the sector, θ is  90° .

Step-by-step explanation:

Given :  

Area of the sector of a circle, A = π cm²

Radius of a circle ,r = 2 cm

Area of the sector of a circle, A = (θ/360) × πr²

π = (θ/360°) π ×2²

π =  (θ/360°) × 4π

π =  (θ/90°) ×π

πθ = 90° π  

θ = 90°  

Angle contained by the sector, θ = 90°  

Hence, the angle contained by the sector, θ is  90° .

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Answer 2

we know that Area of a sector
2πr× angle of sector \ 360°
[ where r = radius of sector ]
${\pi}^{} = \pi \: r \times \frac{angle \: of \: sector \: }{360} \\ 1 = 2 \times 2 \times \frac{angle \: of \: sector \: }{360} \\ 1 = \frac{angle \: of \: sector \: }{90} \\ 90 = angle \: of \: sector$
hence the required solution is 90°