Question

(Calculus) Suppose a forest fire spreads in a circle with radius changing at a rate of 5 feet per minute. At what rate is the area of the burning region increasing when radius reaches 200 feet?

Answer 1

My logic... A = pi r^2

dR/dt = 5 (given)

dA/dr = dA/dr * dr/dt = 2 pi r * 5

dA/dr is therefore 10 pi r

when radius is 200 ft, dA/dr is 2000 pi ft/min

does it look right?

Answer 2

yes it does

Answer 3

Thanks!

Answer 4

I should have written dA/dt = dA/dr * dr/dt...but I think the rest is right.