Chapter 4.5, Problem 254E

The volume of a frustum of a cone is given by the

formula $V=\frac{1}{3}\pi z\left(x^2+y^2+xy\right)$, where x is the radius

of the smaller circle, y is the radius of the larger circle, and is the height of the frustum (see figure). Find the rate of change of the volume of this frustum when

x =10 in. y=12 in.. and z= 18 in.