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Solve the Problem SS (In Square Inches) of a Cylindrical Pipe with Length 12

Question 41

Essay

Solve the problem.
-The surface area SS (in square inches) of a cylindrical pipe with length 12 inches is given by S(r)=2πr2+24πrS ( r ) = 2 \pi r ^ { 2 } + 24 \pi r , 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 surface area SS of the pipe as a function of the time tt .

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