Question

Derive the formula of Area of sector?

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Answer 1

Answer:

In a circle with centre O and radius r, let OPAQ be a sector and θ (in degrees) be the angle of the sector. Area of the circular region is πr². Let this region be a sector forming an angle of 360° at the centre O. Then, the area of a sector of circle formula is calculated using the unitary method.

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Answer 2

Answer:

We know that a full circle is 360 degrees in measurement. Area of a circle is given as π times the square of its radius length. So if a sector of any circle of radius r measures θ, area of the sector can be given by:

Area of sector = θ360×πr2

Derivation:

In a circle with centre O and radius r, let OPAQ be a sector and θ (in degrees) be the angle of the sector.

Area of the circular region is πr².

Let this region be a sector forming an angle of 360° at the centre O.

Then, the area of a sector of circle formula is calculated using the unitary method.

When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr²

When the angle at the center is 1°, area of the sector = π.r23600

Thus, when the angle is θ, area of sector, OPAQ = θ360o×πr2

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