<PRE><B>Question 1119545</B>
&lt;br&gt;
The statement of the problem makes no sense:  &quot;...when the radius is 5 ft is zero.&quot;&lt;br&gt;
I can only assume that the question was supposed to read &quot;... when the radius is 5 feet.&quot;&lt;br&gt;
The formula for the volume of a cylinder is&lt;br&gt;
{{{(pi)(r^2)(h)}}}&lt;br&gt;
The height h is fixed at 10.  The problem asks for the rate of change of volume with respect to diameter; so we need the volume equation in terms of the diameter:&lt;br&gt;
{{{(pi)((d/2)^2)(10) = (5pi/4)(d^2)}}}&lt;br&gt;
Then dV/dd is&lt;br&gt;
{{{(5pi/2)(d)}}}&lt;br&gt;
When the radius is 5, the diameter is 10, so when the radius is 5 the rate of change of volume with respect to diameter is&lt;br&gt;
{{{(5pi/2)(10) = 25pi}}}</PRE>