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Solve the Problem V\mathrm { V } (In Cubic Inches) of a Cylindrical Pipe with Length 12

Question 58

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Solve the problem.
-The volume V\mathrm { V } (in cubic inches) of a cylindrical pipe with length 12 inches is given by V(r)=12πr2\mathrm { V } ( \mathrm { r } ) = 12 \pi \mathrm { r } ^ { 2 } , where rr is the radius of the piston (in inches). If the radius is increasing with time tt (in minutes) according to the formula r(t)=16t2,t0r ( t ) = \frac { 1 } { 6 } t ^ { 2 } , t \geq 0 , find the volume VV of the pipe as a function of the time tt

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