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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 70
Total: 100
A cylinder of height 2x is circumscribed by a sphere of radius 2x such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface area of the cylinder to the surface area of the sphere ?
[2017 CDS-II]
√
3
:
4
√
3
:
3
√
3
:
2
√
3
:
1
Validate
Solution:
Let the radius of the cylinder be r.
Height of the cylinder
= Radius of the sphere = 2x
Now,
(
2
x
)
2
=
x
2
+
r
2
⇒
r
2
=
4
x
2
−
x
2
=
3
x
2
⇒
r
=
√
3
x
∴
Curved surface area of the cylinder
Surface area of the sphere
=
2
π
×
√
3
x
×
2
x
4
π
×
(
2
x
)
2
√
3
4
© examsnet.com
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