Answer
$dV=180\pi=565.4867 in^3$
Work Step by Step
We are given: cylinder height(h)=30 in, radius=6in, and thickness=0.5in
We need to find the change in volume of the cylinder.
The thickness is changing at a rate of (dr)=0.5in
The height is not changing, so dh=0
Volume(V)=$\pi r^2 h$
on differentiating the above equation:
$dV=2\pi rh dr+\pi r^2 dh$
$dV=2\pi 6\times30\times0.5 dr+0$
$dV=180\pi=565.4867 in^3$
Thus, the change in volume of the cylinder is: $180\pi=565.4867 in^3$
