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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 76
Total: 100
Two rectangular sheets of sizes 2π x 4π and π x 5π are available. A hollow right circular cylinder can be formed by joining a pair of parallel sides of any sheet. What is the maximum possible volume of the circular cylinder that can be formed this way ?
[2017 CDS-II]
4
π
2
8
π
2
1.25
π
2
6.25
π
2
Validate
Solution:
Volume of the cylinder formed when sheet of size
2
π
×
4
π
is rolled along the side
2
π
=
π
×
(
2
π
2
π
)
2
×
4
π
=
4
π
2
Volume of the cylinder formed when sheet of size
2
π
×
4
π
is rolled along the side
4
π
=
π
×
(
4
π
2
π
)
2
×
2
π
=
8
π
2
Volume of the cylinder formed when sheet of size
π
×
5
π
is rolled alongthe side
π
=
π
×
(
π
2
π
)
2
×
5
π
=
5
π
2
4
=
1.25
π
2
Volume of the cylinder formed when sheet of size
π
×
5
π
is rolled along the side
5
π
=
π
×
(
5
π
2
π
)
2
×
π
=
25
π
2
4
=
6.25
π
2
© examsnet.com
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