Question

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 V(r) = 0.07πr^2, where r is the radius of the slick in feet. In turn, the radius is increasing over time according to the function r(t) = 0.4t, where t is measured in minutes.

1) find (V of r)(t) and simply it

Answer 1

`V(t)=0.0112\pi t^(2)`

Explanation:

we have

`V(r)=0.07\pi r^(2)` -----> equation A

`r(t)=0.4t` -----> equation B

To find out (V of r)(t) substitute equation B in equation A

`V(r(t))=V(t)`

`V(t)=0.07\pi (0.4t)^(2)`

`V(t)=0.07\pi (0.16)t^(2)`

`V(t)=0.0112\pi t^(2)`