Question

Find the rate of change of the area of a circle with respect to the radius r. What is the rate when r=11?

Answer 1

Area, A = pi (r^2)
To find rate of change, we differentiate area with respect to the radius, 
rate of change = dA/dr = 2 pi (r) 

At r=11, rate of change = 2 pi (r) = 2 pi (11) = 22 pi = 69.1