AREA OF A SECTOR FORMULA

AREA OF A SECTOR FORMULA

Area of sector is the part of the circle enclosed by an arc and two radii drawn to the extremities. Area of a sector can be calculated using the radius(r) and the angle(θ) created by the two radii at the center of the circle. Area of the sector is represented in length – unit2unit2 irrespective of whether the angle given is in degrees or radians. A sector with the central angle of 180° is called a half-disk and is bounded by a diameter and a semicircle. Sectors with other central angles are sometimes given special names, these include quadrants (90°), sextants (60°) and octants (45°), which come from the sector being one 4th or 6th or 8th part of a full circle.

The Area of a Sector Formula is, A = πr2r2(θ360θ360)
Where,
r is the radius of the circle.
θ is the angle created by the two radii at the center of the circle.

SOLVED EXAMPLES

Question 1: Find the area of a sector of a circle whose radius is 8 cm and the angle made at the center of the circle is 45o
Solution:
Given,

r = 8 cm
θθ = 45o
Area of a sector
= πr(θ360θ360)
= π ×× 82 ×× (4536045360) cm2
= π ×× 64 ×× 0.125 cm2
= 25.12 cm2

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