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UPSC CDS 2 2021 Math Paper
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© examsnet.com
Question : 9
Total: 100
A cone of height
16
c
m
and diameter
14
c
m
is mounted on a hemisphere of same diameter. What is the volume of the solid thus formed? (Take
π
=
22
7
)
1540
c
m
3
1078
c
m
3
1048
c
m
3
770
c
m
3
Validate
Solution:
👈: Video Solution
Given, height of the cone,
h
=
16
c
m
diameter of the cone
=
14
c
m
∴
Radius of the cone,
r
=
14
2
=
7
c
m
And diameter of hemisphere
=
14
c
m
∴
Radius of hemisphere,
r
=
14
2
=
7
c
m
Volume of the solid formed = Volume of the cone + volume of hemisphere
=
1
3
π
r
2
h
+
2
3
π
r
3
=
1
3
×
22
7
×
7
×
7
×
16
+
2
3
×
22
7
×
7
×
7
×
7
=
22
×
7
×
16
3
+
2
×
22
×
7
×
7
3
=
22
×
7
3
(
16
+
14
)
=
154
3
×
30
=
1540
c
m
3
Hence, the volume of the solid formed is
1540
c
m
3
.
© examsnet.com
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