The area A of a circle is related to its diameter by the equation `A = (pi)/4 D^(2)` . How fast is the area changing with respect to the diameter when the diameter is 10 m ?

Explanation

The (instantaneous) rate of change of the area with respect to the diameter is `(dA)/(dD) = (pi)/4 2D = (pi D)/2`
When D =10m, the area is changing at rate `(pi//2) = 5pim^(2)//m`. This mean that a small change `DeltaD m` in the diameter would result in a changed of about `5p Delta m^2` in the area of the circle.