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UPSC CDS Math Volume and Surface Area Questions
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© examsnet.com
Question : 95
Total: 104
The volume of a hollow cube is
216
x
3
. The surface area of the largest sphere which can be enclosed in it is
[2014 CDS-I]
18
π
x
2
27
π
x
2
36
π
x
2
72
π
x
2
Validate
Solution:
Let the side of the cube be a units.
∴
a
3
=
216
x
3
=
(
6
x
)
3
⇒
a
=
6
x
Radius of the largest sphere thatcan be inscribed in the cube,
r
=
a
2
=
6
x
2
=
3
x
Surface area of the sphere
=
4
π
2
=
4
π
(
3
x
)
2
=
36
π
x
2
© examsnet.com
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