How fast is the surface area increasing when the length of an edge is 10
centimetres 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