Relation of Rates

Question

The area A = πr² of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3ft?

Options:

1.  6π ft²/ft
2.  3π ft²/ft
3.  6 ft²/ft
4.  9π ft²/ft

Answer 1

A(r) = πr²

dA/dr = 2πr

r = 3 ft ⇒

dA/dr = 2π(3 ft) = 6π ft