Related Rates

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π feet?

• 3 square feet per second

• 2000 square feet per second

• 100 square feet per second

A spherical balloon is inflating at a rate of 27π in³/sec. How fast is the radius of the balloon increasing when the radius is 3 inches?

• 3 in/sec

Cars A and B leave a town at the same time. Car A heads due south at a rate of 80 km/hr and car B heads due west at a rate of 60 km/hr. How fast is the distance between the cars increasing after three hours?

• 100 km/hr

• 3 km/hr

A cylindrical tank with a radius of 6 meters is filling with fluid at a rate of 108π m³/sec. How fast is the height increasing?

• 3 m/sec

An inverted conical container has a diameter of 42 inches and a depth of 15 inches. If water is flowing out of the vertex of the container at a rate of 35π in³/sec, how fast is the depth of the water changing when the height is 5 inches?

• 2000 in/sec

A boat is being pulled toward a dock by a rope attached to its bow through a pulley on the dock 7 feet above the bow. If the rope is hauled in at a rate of 4 ft/sec, how fast is the boat approaching the dock when 25 feet of rope is out?

• 2000 ft/sec

• 100 ft/sec

The radius of a sphere is increasing at a rate of 7.5 m/min. At one instant the radius is 5 m. What is the rate of change of the surface area of the sphere at that instant?

The width of a rectangle is increasing at a rate of 11 cm/hour, and at the same time the length is decreasing at a rate of 9 cm/hour. Currently the width is 3 cm and the length is 8 cm. What is the rate of change of the area of the rectangle at this instant?

• 9 square cm per hour

• 61 square cm per hour

Two cars are driving away from an intersection in perpendicular directions. Car 1's velocity is 7 m/s while Car 2's is 3 m/s. At one point Car 1 is 5 m from the intersection and Car 2 is 12 m away. What is the rate of change of the distance between the two cars?

A 10 ft ladder is sliding down a wall. The base of the ladder is sliding outwards at a rate of 4 ft/s. At the instant the base of the ladder is 8 ft. from the wall, what is the rate that the height of the ladder is changing?

• -3 feet per second

• -4.5 feet per second