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UPSC 2015 CDS I Math Paper
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© examsnet.com
Question : 51
Total: 100
If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone
[2015 CDS-I]
remains unaltered
decreases by 25%
increases by 25%
increases by 50%
Validate
Solution:
Let the original radius and height of the cone be r units and h units, respectively. New radius of the cone
=
R
=
r
−
50
100
×
r
=
r
2
New height of the cone
=
H
=
h
+
200
100
×
h
=
3
h
Volume of the original cone
=
1
3
π
r
2
h
Volume of the new cone
=
1
3
π
(
r
2
)
2
×
3
h
=
3
4
×
1
3
π
r
2
h
Decrease in volume of the cone
=
1
3
π
r
2
h
−
3
4
×
1
3
π
r
2
h
=
(
1
−
3
4
)
×
1
3
π
r
2
h
=
1
4
×
1
3
π
r
2
h
Therefore, percentage decrease in volume of the cone
=
1
4
×
1
3
π
r
2
h
1
3
π
r
2
h
×
100
%
=
25
%
© examsnet.com
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