Solution Let x be the length of a side, V be the volume and S be the surface area of
the cube Then, V = x3 and S = 6x2, where x is a function of time t Now
dV
dt  = 9cm3/s (Given)
Therefore
9 =
3
3
V
(
)
(
)
d
d
d
dx
x
x
dt
dt
dx
dt
=
=
⋅
(By Chain Rule)
=
32
dx
x
dt
⋅
or
dx
dt  =
x32 (1)
Now
dS
dt  =
2
2
(6
)
(6
)
d
d
dx
x
x
dt
dx
dt
=
⋅
(By Chain Rule)
=
32
36
12x
x
x

⋅
=




(Using (1))
Hence, when
x = 10 cm, 
2
3