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Mathematics
Mathematics
Problem
The volume of a cylindrical tank varies with time according to
V
(
t
)
=
π
r
(
t
)
2
h
(
t
)
V(t)=\pi\,r(t)^{2}h(t)
V
(
t
)
=
π
r
(
t
)
2
h
(
t
)
, where the radius and height change with time as follows:
r
(
t
)
=
2
+
0.1
sin
t
meters
,
h
(
t
)
=
5
e
0.05
t
meters
.
\displaystyle r(t)=2+0.1\sin t\ \text{meters}, \qquad h(t)=5e^{0.05t}\ \text{meters}.
r
(
t
)
=
2
+
0.1
sin
t
meters
,
h
(
t
)
=
5
e
0.05
t
meters
.
Calculate
d
V
d
t
\dfrac{dV}{dt}
d
t
d
V
(in cubic meters per second) at
t
=
π
t=\pi
t
=
π
.
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