
Related Rates Practice
Authored by Kent Givens
Mathematics
12th Grade
CCSS covered
Used 28+ times

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8 questions
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1.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A ladder is 10 meters long and is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 meters from the wall?
-1.5 m/s
-2 m/s
3 m/s
0.5 m/s
Tags
CCSS.HSG.SRT.C.8
CCSS.HSA.CED.A.2
2.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A conical tank is being filled with water at a rate of 3 cubic meters per minute. If the tank has a height of 10 meters and a radius of 5 meters, how fast is the water level rising when the water is 6 meters deep?
~ 1/20 m/min
~ 1/10 m/min
~ 1/40 m/min
~ 1/30 m/min
Tags
CCSS.HSG.GMD.A.3
CCSS.HSG.GMD.A.1
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Two cars are approaching an intersection. Car A is 2 km south of the intersection and moving north at 60 km/h, while Car B is 3 km east of the intersection and moving west at 80 km/h. How fast is the distance between the cars changing when Car A is 2 km from the intersection and Car B is 3 km from the intersection?
The distance between the cars is decreasing at a rate of 55 km/h.
The distance between the cars is decreasing at a rate of 70 km/h.
The distance between the cars is decreasing at a rate of 85 km/h.
The distance between the cars is decreasing at a rate of 100 km/h.
Tags
CCSS.HSG.SRT.C.8
CCSS.HSG.SRT.D.11
CCSS.HSN.VM.A.3
4.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 meter higher than the bow of the boat. If the rope is being pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 meters from the dock?
about 1 m/s
about 1.5 m/s
about 2 m/s
about 2.5 m/s
Tags
CCSS.HSG.SRT.C.8
CCSS.HSA.CED.A.2
5.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A plane is flying horizontally at an altitude of 5 km and passes directly over a radar station. If the plane is flying at a speed of 800 km/h, how fast is the distance between the plane and the radar station increasing when the plane is 10 km away from the station (direct, diagonal distance)?
522 km/h
610 km/h
693 km/h
751 km/h
Tags
CCSS.HSG.SRT.C.8
CCSS.HSA.CED.A.2
CCSS.HSG.SRT.C.6
6.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A cylindrical tank with a radius of 4 meters is being filled with water at a rate of 2 cubic meters per minute. How fast is the water level rising when the water is 3 meters deep?
The water level is rising at a rate of 0.04 meters per minute.
The water level is rising at a rate of 0.08 meters per minute.
The water level is rising at a rate of 0.12 meters per minute.
The water level is rising at a rate of 0.16 meters per minute.
Tags
CCSS.HSG.GMD.A.3
7.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
An ice cube is melting in a way such that every side is shrinking at a rate of 1 inch/minute. At what rate is the volume decreasing when the edges of the cube are 4 inches long?
-32 m/s
-48 m/s
-56 m/s
-68 m/s
Tags
CCSS.HSG.SRT.C.8
CCSS.HSA.CED.A.2
CCSS.HSG.SRT.C.6
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