MathCastle
CalculusMediumContextual Applications of Differentiation

Contextual Applications of Differentiation · Medium problem

Water is poured into an inverted conical tank (height 1010 ft, top radius 55 ft) at 33 ft3^3/min. How fast is the water level rising when the depth is 44 ft? (Hint: r=h2r=\tfrac{h}{2}, so V=πh312V=\tfrac{\pi h^3}{12}.) Round to 3 decimal places (an exact answer is also accepted).