<?php $classpath="/213/"; include "../../classes/1.h"; ?>
<title>
11.5 - Ice cream cone / chain rule
</title>
<meta name="week" content="">

<!--meta name="nolink" content="nolink"-->
<?php include "../../classes/2.h" ?>
<link rel="stylesheet" href="0g/handoutprint.css" type="text/css" media="print" />

<style type="text/css">
li {margin-bottom:8ex;}
</style>

<h2>
11.5 - Ice cream and the chain rule
</h2>
<p><img src="0g/11.5.icecream.jpg" class="rightalign">
Consider the solid obtained when rotating the region (right) about the $y$ axis.  The volume of the solid is approximately the volume of ice cream needed to fill and top an ice-cream cone with the dimensions shown.
<ol>
<li>Compute the volume of this solid. (The volume of a cone, though you *can* compute it using calculus, is $V_c=\pi r^2 h/3$.)

<li style="padding-top:10ex">
Find the volume $V(h,r)$ of a similar solid created by rotating a region with dimensions $h$ and $r$ instead of 3 and 2.

<li style="padding-top:10ex">
What's the meaning of $\frac{\del V}{\del r}$?

<li style="padding-top:4ex">
Suppose that $h$ and $r$ are varying with time according to $h(t)=t+\sin t$ and $r(t)=e^t-\cos t$.  Compute $dV/dt$.

<?php $classpath="/213/"; include "../../classes/3.h"; ?>