Question

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

A = πr²
dR/dt = 5 (given)
dA/dr = dA/dr * dr/dt = 2 pi r * 5
 
dA/dr is therefore 10πr when radius is 200 ft, dA/dr is 2000 pi ft/min