Question

The area of a circle is increasing at a rate of 0.4 cm square per second. What is the rate of change of the circumference of the circle when its radius is 5cm?

Answer 1

Answer: 4π cm^2/minute

Explanation:

Rate of change :

Change with respect to time (dr/dt)

dr/dt = 0.4cm^2/s

r = 5cm

The rate of change when the Radius is 5cm

Area / Circumference of a circle (A) = πr^2

From chain rule of differentiation:

dA/dt = (dr/dt) * (dA/dr)

If A = πr^2

dA/dr = 2πr

dA/dr = 2π * 5 = 10π

However,

dA/dt = (dr/dt) * (dA/dr)

dA/dt = (0.4) * (10π)

dA/dt = 4π cm^2/minute