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Test Index
JEE Main Math Class 12 Application of Derivatives Part 2 Questions
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© examsnet.com
Question : 15
Total: 100
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semivertical angle is
tan
−
1
3
4
. Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is _________.
[27-Jul-2022-Shift-2]
Your Answer:
Validate
Solution:
v
=
1
3
π
r
2
h
.
.
.
.
.
(i)
And
tan
θ
=
3
4
=
r
h
.
.
.
.
.
.
. (ii)
i.e. if
h
=
4
,
r
=
3
v
=
1
3
π
r
2
(
4
r
3
)
d
v
d
t
=
4
π
9
3
r
2
d
r
d
t
⇒
6
=
4
π
3
(
9
)
d
r
d
t
⇒
d
r
d
t
=
1
2
π
Curved area
=
π
r
√
r
2
+
h
2
=
π
r
√
r
2
+
16
r
2
9
=
5
3
π
r
2
d
A
d
t
=
10
3
π
r
d
r
d
t
=
10
3
π
⋅
3
⋅
1
2
π
=
5
© examsnet.com
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