Area of Circular Sector
Area of Circular Sector will be find out. When working with circles, it is one of the essential concepts.
What is sector of a circle ?
A sector is a portion of a circle enclosed by two radii and the corresponding arc. In this blog post, we will explore the formula used to calculate the area of a sector and break down its derivation step by step.
Formula for the Area of a Circular Sector
Formula for area of a sector with radius and central angle (in radians):-
$$A\;=\;\frac12r^2\theta$$
If the angle is given in degrees, we will convert it to radians using:
$$1^\circ=\frac\pi{180}\;rad$$
Example Calculation
Let’s calculate the area of a sector with a radius of 5 cm and a central angle of 60 degrees.
- Convert 60 degrees to radians: $$60^\circ=\frac{60\pi}{180}\;rad=\frac\pi3rad$$
- Use the formula: $$A\;=\;\frac12r^2\theta$$
$$A=\frac12{(5)}^2\frac\pi3\\=13.08\;cm^2$$
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Conclusion
This topic is crucial in geometry, physics, and engineering. By following the simple derivation and applying the formula correctly, we can easily calculate the area of any sector given its radius and central angle.
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