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SSC CGL Tier 2 Exam 21 Sep 2014 Paper
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© examsnet.com
Question : 12
Total: 100
A large solid sphere is melted and moulded to form identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to form a smaller solid sphere. Then the ratio of the surface area of the smaller to the surface area of the larger sphere is
1
:
3
4
3
1
:
2
3
2
1
:
3
2
3
1
:
2
4
3
Validate
Solution:
(4) Radius of larger sphere = R units
∴
Its volume
=
4
3
π
R
3
c
u
units
Volume of smaller cone
=
1
3
π
R
3
cubic units
Volume of smaller sphere
=
1
3
π
R
3
∴
4
3
π
r
3
=
1
3
π
R
3
⇒
r
3
=
R
3
4
⇒
r
=
R
3
√
4
∴ Surface area of smaller sphere : Surface area of larger sphere
=
4
π
r
2
:
4
π
R
2
=
r
2
:
R
2
=
(
R
3
√
4
)
2
:
R
2
=
1
:
(
3
√
4
)
2
=
1
:
(
(
2
2
)
1
3
)
2
=
1
:
2
4
3
© examsnet.com
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