​
time
Take the derivative of
V =
4π
3
r
3
to get
∂V
∂t
= 4π
2
r
∂r
∂t
.
Using
∂V
∂t
= 1 and solving,
∂r
∂t
=
1
4π
2
r
.
Also, A = 4π
2
r
,
so
∂A
∂t
= 8πr
∂r
∂t
=
8πr
4π
2
r
=
2
r
.