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A Spherical Weather Balloon Is Being Inflated in Such a Way

question 17

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A spherical weather balloon is being inflated in such a way that the radius is given by r=g(t) =12t+2r = g ( t ) = \frac { 1 } { 2 } t + 2 Assume that r is in meters and t is in seconds, with t = 0 corresponding to the time that inflation begins. If the volume of a sphere of radius r is given by V(r) =43πr3V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 } find the time at which the volume of the balloon is 36πm336 \pi \mathrm { m } ^ { 3 }

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