From the following, which is NOT an equivalent expression to Area of sector is 2πrθ/360. Option A is correct.
The area of the circular sector is the space occupied by it. The area of the circular sector is the half of the product of the angle of the sector and the radius of the circle. It can be given as,
[tex]A_s=\dfrac{r^2\theta}{2}[/tex]
Here, (r) is the radius of the circle and θ is the angle of the sector. Multiply with π/180 to convert it into the degrees.
[tex]A_s=\dfrac{r^2\theta}{2}\left(\dfrac{\pi}{180}\right)\\A_s={\pi r^2}\left(\dfrac{\theta}{360}\right)[/tex]
Thus, the option D is correct. Now, πr² is the area of circle . Thus,
[tex]\rm \text{Area of sector}=\dfrac{(Area\; of \;Circle)(Arc\; Measure)}{360^o}\\\rm \dfrac{(Area\; of \;Sector)}{(Arc\; Measure)}=\dfrac{\text{Area of sector}}{360^o}[/tex]
From the following, which is NOT an equivalent expression to Area of sector is 2πrθ/360. Option A is correct.
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