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UPSC CDS Math Volume and Surface Area Questions
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© examsnet.com
Question : 5
Total: 104
A hollow sphere of external and internal diameters 6 cm and 4 cm respectively is melted into a cone of base diameter 8 cm. What is the height of the cone ?
[2019 CDS-II]
4.75 cm
5.50 cm
6.25 cm
6.75 cm
Validate
Solution:
We have,
External radius of the sphere,
r
1
=
3
c
m
[
∵
diameter
=
2
×
radius
]
Internal radius of the sphere,
r
2
=
2
c
m
Volume of metal in the hollow sphere
=
4
3
π
(
r
1
3
−
r
2
3
)
=
4
3
π
×
(
3
3
−
2
3
)
=
76
π
3
c
m
3
Given that radius of the cone formed,
R
=
4
c
m
.
Let the height of the cone be
h
.
cone
=
1
3
π
R
2
h
Volume of the
=
1
3
π
×
4
2
×
h
=
16
π
h
3
c
m
3
∴
Volume of the cone
=
volume of metal in the sphere
⇒
16
π
h
3
=
76
π
3
⇒
h
=
76
16
=
4.75
© examsnet.com
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