Find dA/dt

Question

Let A be the area of a circle with radius r. If dr/dt= 3, find dA/dt when r = 1.

Answer 1

A = pi*r²

 

To evaluate dA/dt, use the chain rule: dA/dt = (dA/dr)*(dr/dt)

 

dA/dt = pi*2*r*dr/dt

 

Since dr/dt = 3:

 

dA/dt = 6*pi*r

 

When r = 1:

 

dA/dt = 6*pi