The volume of a frustum of a cone is given by the formula
V=(1)/(3)\pi z(x^(2)+y^(2)+xy)
, where
x
is the radius of the smaller circle,
y
is the radius of the larger circle, and
z
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. if
(dz)/(dt)=-5,(dx)/(dt)=1,(dy)/(dt)=1
(all in/min).

Question

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

V=(1)/(3)\pi z(x^(2)+y^(2)+xy)

, where

x

is the radius of the smaller circle,

y

is the radius of the larger circle, and

z

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. if

(dz)/(dt)=-5,(dx)/(dt)=1,(dy)/(dt)=1

(all in/min).

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