1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Area of a Sector of a Circle
The perimeter...
Question
The perimeter of a sector of a circle with central angle 90° is 25 cm. The area of the minor segment of the circle is
(a) 14 cm
2
(b) 16 cm
2
(c) 18 cm
2
(d) 24 cm
2
Open in App
Solution
(a) 14 cm
2
Let r be the radius of the circle and
θ
be the angle.
Now,
Perimeter of the sector
=
2
r
+
2
π
r
θ
360
=
2
r
+
2
×
22
7
×
r
×
90
360
=
2
r
+
11
r
7
=
25
r
7
Also,
25
r
7
=
25
⇒
r
=
25
×
7
25
⇒
r
=
7
cm
Area of the minor segment
=
π
r
2
θ
360
-
1
2
r
2
sin
θ
cm
2
=
22
7
×
7
×
7
×
90
360
-
1
2
×
7
×
7
×
sin
90
°
cm
2
=
77
2
-
49
2
cm
2
=
28
2
cm
2
=
14
cm
2
Suggest Corrections
0
Similar questions
Q.
Find the area and perimeter of a sector with a central angle of
60
∘
in a circle of radius
7
c
m
.
Q.
¯
¯¯¯¯¯¯
¯
O
A
and
¯
¯¯¯¯¯¯
¯
O
B
are perpendicular radii of a circle. If perimeter of minor sector is 20 cm, then find area of the minor segment.
Q.
The areas of the major and the minor sector of a circle are equal when the central angle is
.
Q.
The area of a minor sector of a circle is 3.85 cm
2
and the measure of its central angle is 36
°
. Find the radius of the circle .
Q.
A chord of circle
14
c
m
makes an angle of
60
o
at the centre of the circle. Find
(i) Area of minor sector
(ii) Area of the major segment
(iii)Area of the major sector
(iv)Area of the major segment
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Area of a Sector
MATHEMATICS
Watch in App
Explore more
Area of a Sector of a Circle
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app