A parked car dripping transmission fluid is creating a circular puddle whose area (in square inches) is Aequalspir2 where r is the radius of the circle in inches. Find the rate at which the area of the puddle is increasing at the instant when the radius is 9 inches and increasing at a rate of 3 inches per minute.

dA/dt = 169,56 in²/min

Step-by-step explanation:

We have a circular puddle and its area is:

A = π*r²        (1)            r is the radius of the circular puddle

Differentiating on both sides of the equation we get:

dA/dt  =  π*2*r*dr/dt       (1)

In that expression we know

r = 9 inches    and  dr/dt = 3 in/min. Therefore plugging these values in equation (1)

dA/dt = π*2*9*3

dA/dt = 169,56 in²/min