The rate of change of the volume is 9123 . 185 inches³/min.
What is volume of the sphere?
Volume of sphere is
V = 4/3 π r³
differentiating with respect to time
[tex]\frac{dv}{dt} = \frac{4}{3} \pi . 3r^{2} . \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt} = 4\pi r^{2} . \frac{dr}{dt}[/tex]
now [tex]\frac{dr}{dt} = 6 inches/min ,[/tex] when r = 11
[tex]\frac{dv}{dt} = 4\pi (11)^{2} . 6[/tex]
= 2904 π cubic inches per minute
≅ 9123 . 185 inches³/min
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