Question

using derivative as a rate measure prove the following'if the area of the circle increases at a uniform rate then the rate of increase of the perimeter varies as the radius of the circle'

Answer 1

since a = pi r^2

da/dt = 2pi r dr/dt
Now, if da/dt = a constant k,
2pi r dr/dt = k
dr/dt = k/(2pi r)

since c = 2pi r,
dc/dt = 2pi dr/dt = k/r

So clearly dc/dt changes as r changes