CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

What is the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is 60


A
(3083493) cm2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(3203503) cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
49 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3083 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (3083493) cm2
Given that , radius of circle (r ) = 14 cm

Angle of the corresponding sector. i.e central angle
(θ)=60

In Δ AOB
OA=OB=Radius of circle
Δ AOB is isosceles.

OAB=OBA=θ

Now, in Δ OAB
AOB+OAB+OBA=180

[Since , sum of interior angles of any triangle is 180]

60+θ+θ=180 [given,AOB=60]

2θ=120

θ=60

i.e AOB=OBA=60=AOB

Since, all angles of ΔAOB are equal to 60. So, ΔAOB is an equilateral triangle.

Also, area of ΔAOB
=34×(14)2
[Area of an equilateral triangle=34(side)2]

=34×196
=493 cm2

Area of sector OBAO
=πr2360×θ
=227×14×14360×60
=22×2×146
=22×143
=3083 cm2

The area of the minor segment
= Area of sector OBAO - Area of the equilateral triangle
=(3083493) cm2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle in a semi circle is Right Angle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon