Instantaneous Rate of Change

Question

The oil spilling from the ruptured hull of a grounded tanker spreads in all directions in calm waters. Suppose the area polluted is a circle of a radius r and the radius is increasing at the rate of 2ft/sec.

(a) Find the function f giving the area polluted in terms of r.

(b) Find a function g giving the radius of the polluted area in terms of t.

(c) Find a function h giving the area polluted in terms of t.

(d) What is the size of the polluted area 30 sec after the hull was ruptured?

Answer 1

f(r) = pi*r^2

dG/dt = 2 ---> g(t) = 2t

h = pi*(2t)^2 = 4*pi*t^2

4*pi*30^2 = 3600*pi