Name: ______________________
Related Rates Example WS (#3) (cubes, triangles, angles, cones)
1. A bouillon cube with side length 0.9 cm is placed into boiling water. Assuming it roughly
resembles a cube as it dissolves, at approximately what rate is its volume changing when its side
length is 0 .25 cm and is decreasing at a rate of 0.12 cm/sec?
2.
Two hikers begin at the same location and travel in perpendicular directions. Hiker A travels
due north at a rate of 5 miles per hour; Hiker B travels due west at a rate of 8 miles per hour. At
what rate is the distance between the hikers changing 3 hours into the hike?
3.
A 20-ft. extension ladder propped up against the side of a house is not properly secured,
causing the bottom of the ladder to slide away from the house at a constant rate of 2 ft/sec.
How quickly is the top of the ladder falling at the exact moment the base of the ladder is 12 feet
away from the house?
4.
A camera exactly one mile away from the Space Shuttle’s launch side tracks the ascent of the
spacecraft for a network news program. At what rate is the camera’s angle of elevation
increasing in order to maintain its focus on the shuttle 30 seconds into the launch, once the
shuttle has reached a height of 9,720 feet and is traveling 700 ft/sec? Report your answer in
radians per second accurate to 3 decimal places.
5.
Water is stored in an inverted right circular cone, as illustrated in the figure. The water leaks
out at a constant rate of 2 cubic feet per day (about 15 gallons per day). Assuming the tank is
100 feet high and the radius of its base is 25 feet, at what rate is the depth of the water inside
the tank decreasing at the moment it’s 40 feet deep?