A sector of a circle is like a slice of a circular pizza. The radius of the given circle is 8 units.
How to find the area of a sector of a circle?
A sector of a circle is like a slice of a circular pizza. Its two straight edge's having an angle, and the edge's length(the radius of the circle) are two needed factors for finding the area of that sector.
Since the whole circle with radius 'r' units have 360 degrees angle on the center of the circle, and its area is [tex]\pi r^2 \: \rm unit^2[/tex], thus, as the angle lessens, this area gets lessened.
360 degree => [tex]\pi r^2 \: \rm unit^2 area[/tex]
1 degree =>[tex]\pi r^2 \: \rm unit^2/360 area[/tex]
x degree =>[tex]\dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]
Thus, the area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:
[tex]A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]
In this circle, the area of sector COD is 50.24 square units. Therefore, the area of the sector can be written as,
Area of the sector COD = πR² × (θ/360°)
50.24 units² = πR² × (90/360)
(50.24×360)/(90×π) = R²
R² = 63.96755
R = 7.9979 ≈ 8 units
Hence, the radius of the circle is 8 units.
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