An oil well off the Gulf Coast is leaking, with the leak spreading oil over the
ID: 2911524 • Letter: A
Question
An oil well off the Gulf Coast is leaking, with the leak spreading oil over the water's surface as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the circular oil slick on the surface is r(t) equals = 3t feet. Let A(r) equals = (pi r squared) r^2 represent the area of a circle of radius r.
(a) Find (A r)(t).
(b) Interpret (A r)(t).
(c) What is the area of the oil slick after 3 min?
(a) (A circle r)(t) = (Simplify your answer. Type an exact answer, using pi as needed.)
(b) It defines _____ in terms of ____ .
(c) The area of the oil slick after 3 min is _____ ft^2. (Simplify your answer. Type an exact answer, using pi as needed.)
Explanation / Answer
r(t) = 3t
A(r) = pir^2
a) (Aor)(t) = pi ( 3t)^2
= 9pit^2
b) it defines area in terms of time
c) area of the slick after 3 min
area = 9pi(3)^2
= 81pi