Question

Let $V$ be the volume of a cylinder having height $h$ and radius $r,$ and assume that $h$ and $r$ vary with time. (a) How are $d V / d \tau, d h / d t,$ and $d r / d t$ related? (b) At a certain instant, the height is 6 in and increasing at 1 in/s, while the radius is 10 in and decreasing at 1 in $/ \mathrm{s}$ How fast is the volume changing at that instant? Is the volume increasing or decreasing at that instant?

          Let $V$ be the volume of a cylinder having height $h$ and radius
$r,$ and assume that $h$ and $r$ vary with time.
(a) How are $d V / d \tau, d h / d t,$ and $d r / d t$ related?
(b) At a certain instant, the height is 6 in and increasing at 1 in/s, while the radius is 10 in and decreasing at 1 in $/ \mathrm{s}$ How fast is the volume changing at that instant? Is the volume increasing or decreasing at that instant?

Added by Michael B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

Let $V$ be the volume of a cylinder having height $h$ and radius $r,$ and assume that $h$ and $r$ vary with time. (a) How are $d V / d \tau, d h / d t,$ and $d r / d t$ related? (b) At a certain instant, the height is 6 in and increasing at 1 in/s, while the radius is 10 in and decreasing at 1 in $/ \mathrm{s}$ How fast is the volume changing at that instant? Is the volume increasing or decreasing at that instant?