Math, asked by sonujaju2346, 10 months ago

area of segment of circle of radius 21 CM if the arc of the segment has a measure of 60 degree is​

Answers

Answered by 6161amanchauhan
2

Answer:

Step-by-step explanation:

Length of arc APB =teta/360° ×2pi r

=22cm

Answered by slicergiza
3

The area would be (231 -\frac{441}{4}\sqrt{3}) cm²

Step-by-step explanation:

Consider O is the center of the circle and A, P and B are points of the circumference of the circle. ( shown in below diagram )

Given,

The radius of the circle, r = 21 cm,

Angle made by arc AB in circle, \theta = 60°,

Thus, the area of the sector OAPB formed by the arc

=\frac{\theta}{360^{\circ}} \pi r^2

=\frac{60^{\circ}}{360^{\circ}} \pi (21)^2

=\frac{1}{6} \frac{22}{7}(21)^2

=\frac{11}{3}\times 21\times 3

=11\times 21

= 231 cm²

Now, area of a triangle having adjacent sides s_1 and s_2 with included angle \theta is,

A=\frac{1}{2}\times s_1\times s_2\times \sin \theta

So, the area of triangle OAB

=\frac{1}{2}\times OA\times OB\times \sin \theta

=\frac{1}{2}\times 21\times 21\times \sin 60^{\circ}

=\frac{441}{2}\times \frac{\sqrt{3}}{2}

=\frac{441\sqrt{3}}{4}\text{ square cm}

Hence, the area of chord APB = Area of OAPB - area of triangle OAB

=(231 -\frac{441}{4}\sqrt{3})\text{ square cm}

#Learn more:

What is segment of a circle?how to find the area of segment of a circle?​

https://brainly.in/question/11559724

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