Engineering Board Exam Reviewer · Related Rates (Time Rates) · medium
The length of a rectangle is increasing at 3 cm/s while its width is decreasing at 2 cm/s. At what rate is the area changing when the length is 10 cm and the width is 6 cm?
- 2 cm2 /s
- -2 cm2 /s
- 18 cm2 /s
- -20 cm2 /s
Answer
B. -2 cm2 /s
Solution
A=lw /dt=dl/dtw+ldw/dt=3(6)+10(-2)=18-20=-2 cm2/s (the area is decreasing).
More Related Rates (Time Rates) questions
- A ladder 10 ft long leans against a vertical wall. If the bottom slides away from the wall at 2 ft/s, how fast is the top sliding down the…
- A spherical balloon is being inflated at a rate of 100 cm3/s. Find the rate of change of the radius when the radius is 5 cm.
- Water is poured into a conical tank (vertex down) at a rate of 12 m3/min. The tank has a height of 10 m and a top radius of 5 m. Find the…
- A man 6 ft tall walks away from a lamp post 18 ft high at a rate of 5 ft/s. Find the rate at which his shadow is lengthening.
- For the same man and lamp post as above (man 6 ft tall, post 18 ft, walking at 5 ft/s), find the rate at which the tip of his shadow is…
- A boat is pulled toward a dock by a rope passing through a pulley on the dock 8 ft above the water. If the rope is pulled in at 3 ft/s…
- A kite is flying at a constant height of 60 ft and moving horizontally away from the person flying it at 5 ft/s. Find the rate at which…
- A stone dropped into a still pond sends out a circular ripple whose radius increases at 1.5 ft/s. Find the rate at which the enclosed area…
- Air is pumped into a spherical balloon so that its volume increases at 200 cm3/s. How fast is the radius increasing when the diameter is…
- Sand falls off a conveyor belt onto a conical pile at 10 ft3/min. The diameter of the base of the cone is always three times the height…