AP Calculus AB - Related Rates Review
1
A 26-ft ladder leans against a wall. The bottom of the ladder slides away from the wall at a rate of 3 ft/sec. Find the
rate at which the top of the ladder is moving down the wall when the bottom of the ladder is 10 feet from the wall.
2
A 20-ft ladder is sliding down the side of a building. The bottom of the ladder slides away from the building at a rate
of 4 ft/sec. At what rate is the top of the ladder sliding down when the bottom is 12 feet from the building?
3
A 13-ft ladder leans against a building. The bottom of the ladder forms an acute angle with the ground. If the
bottom of the ladder slides away from the building at a rate of 2 ft/sec, at what rate is the aforementioned angle
changing when the bottom is 5 feet from the building?
4
A spherical balloon is being filled with helium so that the radius is increasing at a rate of 14 in/min. Determine the
rate at which the volume of the balloon is changing when the radius is 8 inches.
5
A spherical balloon is being filled with helium at a rate of 128 in 3 / min. Find the rate at which the radius is changing
when the radius is 4 inches.
6
The radius of a circular oil slick on the surface of the ocean is expanding at a rate of 2 m/min. How fast is the area of
the oil slick increasing when the radius is 25 m?
7
A cylindrical bucket with radius 4 inches is being filled with water at a rate of 3 in 3 / min. How fast is the height of
the water increasing?
8
Each side of a square is increasing at a rate of 6 cm/sec. At what rate is the area of the square increasing when the
length of the sides is 4 cm?
9
Water is flowing at the rate of 50 m3 / min from a reservoir in the shape of an inverted cone. The height of the cone
is 6 m, while the radius at the top is 45 m. How fast is the water level falling when the water is 5 meters deep?
10 A conical tank (vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of
10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.
11 A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. At what rate
is the length of the man’s shadow changing when he is 10 feet from the light?
12 A man 6 feet tall walks at the rate of 4 feet per second toward a streetlight that is 16 feet above the ground. At what
rate is the length of his shadow changing when he is 12 feet from the light?
Answers
4
1)
ft/sec
5
4) 2584 in3 / min
3
in/min
16
9
10)
ft/min
10
7)
2) 3 ft/sec
1
in/min
2
8) 48 cm2 /min
5)
11)
10
ft/sec
3
1
rad/sec
6
6) 100 m2 /min
3) 
8
m/min
225
12
12) 
ft/sec
5
9)