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Cube Balloon Volume Rate Calculus

1425ApprenticeCalculus

Harvard-MIT Math Tournament

A balloon that blows up in the shape of a perfect cube is being blown up at a rate such that at time $t$ fortnights, it has surface area $6 t$ square furlongs. At how many cubic furlongs per fortnight is the air being pumped in when the surface area is $144$ square furlongs?
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