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VITEEE 2019 Solved Paper
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© examsnet.com
Question : 94
Total: 125
The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm
3
/min, when the radius is 2 cm and the height is 3 cm is
-2π
−
8
π
5
−
3
π
5
2
π
5
Validate
Solution:
Given
V
=
π
r
2
h
.
Differentiating both sides, we get
d
V
d
t
=
π
(
r
2
d
h
d
t
+
2
r
d
r
d
t
h
)
=
π
r
(
r
d
h
d
t
+
2
h
d
r
d
t
)
d
r
d
t
=
1
10
and
d
h
d
t
=
−
2
10
d
V
d
t
=
π
r
(
r
(
−
2
10
)
+
2
h
(
1
10
)
)
=
π
r
5
(
−
r
+
h
)
Thus, when r = 2 and h = 3,
d
V
d
t
=
π
(
2
)
5
(
−
2
+
3
)
=
2
π
5
© examsnet.com
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