## University Calculus: Early Transcendentals (3rd Edition)

$dV=180\pi=565.4867 in^3$
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: $180\pi=565.4867 in^3$