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Mathematics
Problem
For a cube whose edge length (in cm) varies with time
t
t
t
(in s) according to
a
(
t
)
=
2
t
+
t
2
a(t)=2t+t^{2}
a
(
t
)
=
2
t
+
t
2
, answer the following at
t
=
2
s
t=2\,\text{s}
t
=
2
s
: a. (i) Calculate
d
a
d
t
\dfrac{da}{dt}
d
t
d
a
. b. (ii) Hence find
d
V
d
t
\dfrac{dV}{dt}
d
t
d
V
. c. (iii) Determine the rate of change of the total surface area of the cube.
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