# Using Implicit Differentiation to Solve Related Rates Problems - Page 2

Questions

- A spherical balloon is expanding at the rate of 60pi cubic inches per second. How fast is the surface area of the balloon expanding when the radius of the balloon is 4 in?
- If #x^2+y^2=25# and #dy/dt=6#, how do you find #dx/dt# when #y=4# ?
- Assume the bottom of a 16 ft ladder is pulled out at a rate of 3 ft/s. How do you find the rate at the top of the ladder when it is 10 ft from the ground?
- How much salt is in the tank after t minutes, if a tank contains 1000 liters of brine with 15kg of dissolved salt and pure water enters the tank at 10 liters/min?
- How do you find the rate at which water is being pumped into the tank in cubic centimeters per minute if water is leaking out of an inverted conical tank at a rate of 12500 cubic cm/min at the same time that water is being pumped into the tank at a constant rate, and the tank has 6m height and the the diameter at the top is 6.5m and if the water level is rising at a rate of 20 cm/min when the height of the water is 1.0m?
- The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 40 mm?
- If a hose filling up a cylindrical pool with a radius of 5 ft at 28 cubic feet per minute, how fast is the depth of the pool water increasing?
- At what rate, in cm/s, is the radius of the circle increasing when the radius is 5 cm if oil is poured on a flat surface, and it spreads out forming a circle and the area of this circle is increasing at a constant rate of 5 cm2/s?
- A plane flying horizontally at an altitude of 1 mi and a speed of 540 mi/h passes directly over a radar station. How do you find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station?
- A hypothetical square shrinks so that the length of its diagonals are changing at a rate of −8 m/min. At what rate is the area of the square changing when the diagonals are 5 m each?
- How fast is the radius of the basketball increasing when the radius is 16 cm if air is being pumped into a basketball at a rate of 100 cm3/sec?
- Two sides of a triangle are 6 m and 7 m in length and the angle between them is increasing at a rate of 0.07 rad/s. How do you find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is pi/3?
- Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at 25mi/h. At what rate is the distance between the cars increasing two hours later?
- CALCULUS RELATED RATE PROBLEM. PLEASE HELP??
- A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 13 km and climbs at an angle of 40 degrees. At what rate is the distance from the plane to the radar station increasing 4 minutes later?
- A hypothetical square shrinks at a rate of 2 m²/min. At what rate are the diagonals of the square changing when the diagonals are 7 m each?
- A plane flying horizontally at an altitude of 1 mi and speed of 500mi/hr passes directly over a radar station. How do you find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station?
- The radius of a spherical balloon is increasing by 5 cm/sec. At what rate is air being blown into the balloon at the moment when the radius is 13 cm?
- A conical tank is 8m high. The radius at the top is 2m. At what rate is water running out if the depth is 3m and is decreasing at the rate of 0.4 m/min?
- A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 8 in?