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JEE Advanced 2015 Paper 1
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© examsnet.com
Question : 48
Total: 60
A cylindrical container is to be made from certain solid material with the following constraints.It has a fixed inner volume of V and
m
m
3
,has a 2 mm thick solid wall and is open at the top.The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container
If the volume of the material used to make the container in minimum when the inner radius of the container is 10mm,then the value of
V
250
π
is
1
4
3
9
Validate
Solution:
Let inner radius be r and the inner length l
π
r
2
l
=
V
Volume of the material be M
M
=
π
(
r
+
2
)
2
(
l
+
2
)
−
π
r
2
l
d
M
d
r
=
−
4
V
r
2
−
8
V
r
3
+
8
π
+
0
+
4
π
r
d
M
d
r
=
0
where
r
=
10
⇒
V
=
1000
π
⇒
V
250
π
=
4
© examsnet.com
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