Question

A fire has started in a dry open field and is spreading in the form of a circle. If the radius of this circle increases at the rate of 6ft/min, express the toatal fire area A as a function of time t (in minutes

Answer 1

"the radius of this circle increases at the rate of 6ft/min" tells us
dr/dt = 6
then r = 6t + c
but when t=0, r was probably zero, so c=0
r = 6t
but Area of circle = pir^2
= pi(6t)^2

= 36pi(t^2)

Answer 2

thank you! but what do
"dr" and "dt" mean?

Answer 3

and "c"?

Answer 4

Are you not in Calculus?
What grade level is this from?

dr/dt is the rate of change of r, the radius in feet, with respect to t, the time in minutes

my little equation of r = 6t should be easy to understand without knowing Calculus
e.g. in 2 minutes, the radius would be 12 feet. (r = 6(2) )
in 4 minutes it would be r = 6(4) or 24 feet.