Question

The radius of a circular puddle is growing at a rate of 25 cm/s. How fast is the area growing at the instant when it equals 81 cm?

Answer 1

The area of a circular puddle is Pi * r^2

Answer 2

so 81=pi(25)^2?

Answer 3

The area of the puddle changes as the radius changes, but the radius changes as time changes or elapses.

Answer 4

da/dt=pi*r^2? I'm not really sure how to set up the equation

Answer 5

Area changes with radius, but radius changes with time

Answer 6

thats a chain rule

Answer 7

d/dt A(r(t)) = dA/dr * dr/dt

Answer 8

or more simply we can write
dA/dt = dA/dr * dr/dt

Answer 9

let u = g(t)

[f(u)] ' = f ' (u) * du/dt

Answer 10

Okay, I'm not sure how to do it with the chain rule. I thought the setup would be something like dA/dt=2pi * r * dr/dt
Would that be correct also?

Answer 11

And then find dA/dt?

Answer 12

yes that is correct