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

Answer:

$V(t)=0.0112\pi t^{2}$

Step-by-step 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

$V(r(t))=V(t)$

$V(t)=0.07\pi (0.4t)^{2}$

$V(t)=0.07\pi (0.16)t^{2}$

$V(t)=0.0112\pi t^{2}$