Answer:
[tex](V(r))(t)=0.0112\pi t^{2}[/tex]
Step-by-step explanation:
Given : An accident at an oil drilling platform is causing a circular-shaped oil slick to form. The volume of the oil slick is roughly given [tex]V(r) = 0.07\pi r^2[/tex], where r is the radius of the slick in feet. In turn, the radius is increasing over time according to the function [tex]r(t)=0.4t[/tex] where t is measured in minutes.
To find : (V of r)(t) and simply it ?
Solution :
Let [tex]V(r) = 0.07\pi r^2[/tex] ....(1)
and [tex]r(t)=0.4t[/tex] ....(2)
For (V of r)(t)=V(r(t)) substitute equation (2) in (1),
i.e. [tex]V(r(t))=V(0.4t)[/tex]
[tex]V(r(t))=0.07\pi (0.4t)^2[/tex]
[tex](V(r))(t)=0.07\pi (0.16)t^{2}[/tex]
[tex](V(r))(t)=0.0112\pi t^{2}[/tex]
