The change in volume is -88π
The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.
Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement
The radius is decreasing at 2 inches per minute
The height is given as decreasing at 4 inches per minute
So let [tex]\frac{dr}{dt}=-2[/tex] and
[tex]\frac{dh}{dt}=-4[/tex]
and we have radius r=6,
height h=5
The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]
Then
[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]
[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]
[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]
So the volume change is [tex]-88\pi[/tex]
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