Question

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

Answer 1

Answer:

Step-by-step explanation:

Length of arc APB =teta/360° ×2pi r

=22cm

Answer 2

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?​

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