Question

Find the area of the sector of a circle with radius 4 cm and angle 30 degree.

Answer 1

Area total: 16π
30° is 360/12 ( total angle of circle 360)
Area of sector: 16π/12= 4.188

Answer 2

$\huge\star{\red{\underline{\mathfrak{Answer :-}}}}$

$4.19 \: {cm}^{2} (approx.)$

$\huge\star{\red{\underline{\mathfrak{Explanation :-}}}}$

Given :-

Radius of the circle = 4 cm

The angle of the sector OAPB = 30°

To find :-

The area of the sector OAPB.

Solution :-

The formula to find the area of the sector is :-$\frac{\pi {r}^{2} \theta}{360}$

$= 3.14 \times \frac{1}{360} \times {4}^{2}$

$= \frac{12.56}{3}$

$= 4.19 \: {cm}^{2}$

The area of sector = 4.19 cm^2

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Related formulas :-

• Area of circle =$\pi {r}^{2}$

• Circumference of circle =$2\pi \times r$

• Area of sector =$\frac{\pi {r}^{2} \theta}{360}$

• Area of a circular ring also called as annulus =$\pi( {R}^{2} - {r}^{2} )$

• Length of the arc of a sector =$\frac{\pi {r} \theta}{180}$

• Segment's Area = area of the sector - area of the triangle.

• Area of the segment if theta is equal to or less than 90 degrees = $\frac{\pi {r}^{2} \theta}{360} - \frac{ {r}^{2} \sin\theta }{2}$

• Area of segment if theta is more than 90 degrees =$\frac{\pi {r}^{2} \theta}{360} - {r}^{2} \sin( \frac{\theta}{2} ) \cos( \frac{\theta}{2} )$

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