Final answer:
The rate at which the area changes when the radius of the plate is 1/π cm is 4 cm^2/s.
Step-by-step explanation:
To find the rate at which the area changes, we can use the derivative of the area formula.
The area of a circle is given by A = πr^2, where r is the radius.
We are given that the radius is changing at a rate of 2 cm/s, so we can substitute this value into the derivative.
dA/dt = 2πr(dr/dt)
Plugging in r = 1/π cm and dr/dt = 2 cm/s, we can calculate the rate at which the area changes.
dA/dt = 2π(1/π)(2) = 4 cm^2/s