Question

The radius of a circle increases at a constant rate of 0.2m/s. What is the rate of increase in the area of the circle when the circumference is 20(pi)m?

Answer 1

dr/dt = 0.2 m/s
A = pi r^2
Take the derivative of the area formula.
dA/dt = 2pi*r dr/dt
20pi = 2pi*r
r = 10, plug that in
rate of area increase = 2pi(10)(0.2)
=4pi

Answer 2

Thank you :)