[Math] rate of change of area of circle per second w.r.t. radius

Question

Find the rate of change of the area of a circle per second with
respect to its radius when radius=5cm.

Source

$A= \pi r^2$ ⇒ $\frac{{\rm d}A}{{\rm d}r} =2rπ$

So when $r=5$cm, $\frac{{\rm d}A}{{\rm d}r}= 10 \pi$ cm

But the answer is $10\pi$ cm$^2$/sec. I don't understand how time comes into picture when we are only talking about radius and area? Why is "per second" even mentioned in the question?

Answer 1

Find the rate of change of the area of a circle per second when its radius of 5 cm is expanding at rate of 1 cm per second.

... such a question would be better