If the area of circle increases at a uniform rate, then prove that theperimeter varies inversely as the radius.

If the area of circle increases at a uniform rate, then prove that the

1.	If the area of circle increases at a uniform rate, then prove that theperimeter varies inversely as the radius.
Answer» Area of a circle, `A = pir^2` `:. (dA)/dt = 2pir (dr)/dt` It is given that area of circle increases at uniform rate. `:. (dA)/dt = k`, where `k` is a constant. `=> 2pir (dr)/dt = k` `=> (dr)/dt = k/(2pir)` Now, perimeter of the circle `P = 2pir` `:. (dP)/dt = 2pi(dr)/dt` `=> (dP)/dt = (2pi)(k/(2pir)) = k/r` Thus, rate of change of perimeter varies inversely with the radius.