Section 4.6 Related Rates. Consider the following problem: –A spherical balloon of radius r centimeters has a volume given by Find dV/dr when r = 1 and.

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Section 4.6 Related Rates

Consider the following problem: –A spherical balloon of radius r centimeters has a volume given by Find dV/dr when r = 1 and when r = 2 and give a practical interpretation of your answers. Suppose that the balloon is being inflated in such a way that r(t) = 2t centimeters after t seconds. How fast is the volume of the balloon increasing when r = 1? When r = 2? Air is being blown in the balloon at a constant rate of 50 cubic centimeters per second. How fast is the radius of the balloon increasing when r = 1? When r = 2?

A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?

A water tank has the shape of an inverted circular cone with base radius 2m and height 4m. If water is being pumped into the tank at a rate of 2m 3 /min, find the rate at which the water level is rising when the water is 3m deep.