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UPSC CDS Math Volume and Surface Area Questions
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© examsnet.com
Question : 29
Total: 104
A cube of maximum volume (each corner touching the surface from inside) is cut from a sphere. What is the ratio of the volume of the cube to that of the sphere ?
[2018 CDS-I]
3
:
4
π
√
3
:
2
π
2
:
√
3
π
4
:
3
π
Validate
Solution:
Let the side of the cube be a and the radius of the square be r.
Then,
√
3
a
=
2
r
(for maximum volume of the diagonal of cube will be equal to diameter)
⇒
a
r
=
2
√
3
∴
Volume of cube
Volume of sphere
=
a
2
4
3
π
r
3
=
3
4
π
×
(
a
r
)
2
=
3
4
π
×
8
3
√
3
=
2
√
3
π
© examsnet.com
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