Question

Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm.

Answer 1

As we know that area of a circular disc = πr² and circumference of a circular disc = 2πr

Here r = radius of circular disc

To find dA/dC here A = area of circular disc and c = circumference of the circular disk.

dA/dC = (dA/dr) x (dr/dC) 

dA/dr = 2πr

dC/dr = 2π

dA/dC = 2πr/2π = r

(dA/dr)_{at x = 3} = 3cm