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UPSC 2014 CDS I Math Paper
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© examsnet.com
Question : 74
Total: 100
A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between
[2014 CDS-I]
370
c
m
3
a
n
d
380
c
m
3
380
c
m
3
a
n
d
390
c
m
3
390
c
m
3
and
400
c
m
3
None of the above
Validate
Solution:
Height of the hemisphere = Radius of the hemisphere = 3.5 cm
Height of the cone
=
12.8
–
(
3.5
+
6.5
)
=
2.8
c
m
V = Volume of the structure = Volume of hemisphere + Volume of cylinder + Volume of cone
=
2
3
π
(
3.5
)
3
+
π
(
3.5
)
2
×
6.5
+
1
3
π
(
3.5
)
2
×
2.8
=
1
3
×
22
7
×
(
3.5
)
2
×
(
7
+
19.5
+
2.8
)
=
376.02
c
m
3
(approx)
∴
370
c
m
3
<
V
<
380
c
m
3
© examsnet.com
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