Science:Math Exam Resources/Courses/MATH102/December 2013/Question C 01/Statement

A mollusc grows inside a shell and produces new shell material at its opening (indicated in the image below in bold)

The volume of the shell can be approximated as that of a cone of base radius r and height h.

Given that the height of the cone grows at a constant rate of 0.1 cm/year, at what rate will the volume of the cone be changing when $h=10$ and $r=1$ cm? Leave your answer in terms of $\pi$.

Note that:

$V_{\text{cone}}={\frac {1}{3}}\pi r^{2}h$