Calculus/Related Rates/Solutions

1. A spherical balloon is inflated at a rate of . Assuming the rate of inflation remains constant, how fast is the radius of the balloon increasing at the instant the radius is ? Known: Take the time derivative: Solve for : Plug in known values: 2. Water is pumped from a cone shaped reservoir (the vertex is pointed down) in diameter and deep at a constant rate of . How fast is the water level falling when the depth of the water is ? Known: Take the time derivative: Solve for : Plug in known values: 3. A boat is pulled into a dock via a rope with one end attached to the bow of a boat and the other wound around a winch that is in diameter. If the winch turns at a constant rate of , how fast is the boat moving toward the dock? Let be the number of revolutions made and be the distance the boat has moved toward the dock. Known: (each revolution adds one circumferance of distance to s) Solve for : Take the time derivative: Plug in known values: 4. At time a pump begins filling a cylindrical reservoir with radius 1 meter at a rate of cubic meters per second. At what time is the liquid height increasing at 0.001 meters per second? Known: Take the time derivative: Plug in the known values: Solve for t: