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UPSC 2014 CDS I Math Paper
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© examsnet.com
Question : 92
Total: 100
What is the area of the larger segment of a circle formed by a chord of length 5 cm subtending an angle of 90° at the centre ?
[2014 CDS-I]
25
4
(
π
2
+
1
)
c
m
2
25
4
(
π
2
−
1
)
c
m
2
25
4
(
3
π
2
+
1
)
c
m
2
None of the above
Validate
Solution:
Let the radius of the circle be r cm.
r
2
+
r
2
=
5
2
⇒
2
r
2
=
25
⇒
r
=
5
√
2
c
m
Therefore, area of the larger segment = Area of the sector with central angle 270° + Area of ΔOAB
=
270
°
360
°
×
π
(
5
√
2
)
2
+
1
2
×
5
√
2
×
5
√
2
=
3
4
×
π
×
25
2
+
25
4
=
25
4
(
3
π
2
+
1
)
c
m
2
© examsnet.com
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