A SECTOR is an area inside a circle which is enclosed by an arc and two radii with a certain angle.
Recall that in finding the AREA OF A SECTOR, we use the formula
A = (1/2)(r^2)(Θ)
where A is the area;
r is the radius; and
Θ is the angle in radians
Note that the angle is in "radians", so we should convert the given angle into radians. RADIAN is the standard unit used in angular measurements, and is also the SI unit in measuring angles. CONVERTING DEGREES TO RADIANS, we use the conversion factor π radians is equal to 180 degrees.
We first convert 60 degrees to radians
Θrad = (60°)( π rad / 180°)
Θrad = π/3 rad
Substituting the values in the equation, we have
A = (1/2)(9cm)^2(π/3)
A = π
Therefore, the area of the sector is π or approximately 42.41 cm^2
For more related problems involving area of sectors, see links below.
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A sector is like a "pizza slice" of the circle. It consists of a region bounded by two radii and an arc lying between the radii.
The area of a sector is a fraction of the area of the circle. This area is proportional to the central angle. In other words, the bigger the central angle, the larger is the area of the sector.
Formula for Area of Sector (in degrees)
We will now look at the formula for the area of a sector where the central angle is measured in degrees.
Recall that the angle of a full circle is 360˚ and that the formula for the area of a circle is πr2.
Comparing the area of sector and area of circle, we derive the formula for the area of sector when the central angle is given in degrees.
where r is the radius of the circle
This formula allows us to calculate any one of the values given the other two values.