Question

Find the area of the segment of a circle of radius 14cm, if the length of the corresponding arc is 22cm.

Answer 1

area of any circular arc= (angle at centre /2) *r²

central angle = arc length /radius
here

central angle =22/14

are of arc. =(22/14) /2 * (14²)
=11* 14
154cm²
hope it helps u bro

Answer 2

Answer:

Area of the segment = 56 cm²

Step-by-step explanation:

$\textbf{Area of any circular arc =}\frac{\text{angle at centre}}{2}\times r^2\\\\\text{Central angle = }\frac{\text{arc length}}{\text{radius}}\\\\\implies \text{central angle = }\frac{22}{14} \\\text{Now, Area of arc ACBO = }\frac{\frac{22}{14}}{2}\times 14^2  =11\times 14=154\thinspace cm^2\\\\\text{Area of triangle AOB = }\frac{1}{2}\times OA\times OB\\\\Area = \frac{1}{2}\times 14\times 14=98\thinspace cm^2$

Now, area of the required segment = are of arc ACBO - Area of triangle AOB

Required Area = 154 - 98 = 56 cm²