The volume V (in cubic inches) of a cylindrical pipe with length 12 inches is given by V(r)= 12 πr^2, where r is the radius of the piston (in inches.) If the radius is increasing with time t (in minutes) according to the formula r(t)=1/6t^2, where t>0 (greater than or equal to 0), find the volume of the pipe as a function of the time t.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.