Question

Derive the formula used to find the area of sector and lenght of arc of sector.

Answer 1

Step-by-step explanation:

area of sector= πr^2theta/360.

length of arc = 2πrtheta/ 360

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Answer 2

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Circle is also a sector subtending an angle of 360° at the centre.

So, when the degree measure of the angle at the centre is 1, area of the sector

$= \frac{\pi r^{2}}{360}$

Therefore, when the degree measure of the angle at the centre is 0,

Area of the sector

$= \frac{\pi r^{2}}{360} × 0 = \frac{0}{360} × \pi r^{2}$

Arc of a sector is a part of the circumference.

When the degree measure of the angle at the centre is 1, the length of the arc

$= \frac{2 \pi r}{360}$

Therefore, when the degree measure of the angle at the centre is 0,

Length of the arc

$= \frac{2 \pi r}{360} × 0 = \frac{0}{360} × 2 \pi r$