1) The area of an equilateral triangle is decreasing at 4 cm^2/min when the area is 200 cm^2. Find the rate of change of the length of a side b at this time. 2) A truck is traveling at 65 mph along a highway parallel to a radio transmitter 3 miles away. Find the rate of change of the distance between the truck and transmitter when they are 5 miles apart. 3) A 13-ft ladder is sliding away from a house at 5 ft/sec when its base is 12 ft from the house. Find the rate of change of the height of the top of the ladder at this time.

1. Names____________ _____________
Calculus BC Group Test
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Related Rates
1) The area of an equilateral triangle is decreasing at a rate of 4 cm2/min. Find the rate at which the
length of a side b is changing when the area of the triangle is 200 cm2. Area of an equilateral triangle
3 2
equals b .
4
2) A radio transmitter is located 3 miles from a straight section of interstate highway. A truck is
traveling along the highway at a speed of 65 miles per hour. How fast is the distance between the
truck and the transmitter changing when they are 5 miles apart?
3) A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is
12 ft from the house, the base is moving at the rate of 5ft/sec. How fast is the top of the ladder sliding
down the wall at that moment?
4) A spotlight shines on a wall forming a cone of light in the air. The light is being moved closer to the
wall, making the length of the cone decrease at 6 ft/min. At the same time, the light is being refocused,
making the radius of the cone increase at 7 ft/min. At the instant when the length is 3 ft and the radius
is 8 ft, is the volume of the cone increasing or decreasing? How fast? Volume of a cone equals
1 2
πr h .
3
3
5) Water is flowing at the rate of 50 min from a concrete conical reservoir (vertex down) of base radius
m
4.5m and height 6m. How fast is the radius of the water’s surface changing when the water is 5m
deep?
6) A street light is mounted to the top of a 14 ft pole. A woman 6 ft tall walks away from the pole with
a speed of 4 ft/s along a straight path. How fast is the tip of her shadow moving when the woman is
30ft from the pole?
7) A kite 100 feet above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle
between the string and the ground decreasing when 200 feet of kite string have been let out?
8) A Ferris wheel, 50 feet in diameter, revolves at the rate of 10 radians/min. How fast is a passenger
rising vertically when he is 15ft higher than the center of the Ferris wheel and going up?