Related Rates Problems
1. If 2x + 3y = 8 and dy/dt= 2, compute dx/dt.
2. If xy = 20 and dy/dt = 10 find dx/dt when x = 2.
3. If sin 2x + cos 2y = 5/4 and dx/dt = -1, find dy/dt at (2/3 π, 3/4π)
4. A spherical snowball is being made so that its volume is increasing at the rate of 8 cubic feet per
minute. Find the rate at which the radius is increasing when the snowball is 4 feet in diameter.
5. A light is hung 15 ft above a straight horizontal path. If a man 6 ft tall is walking away from the light
at the rate of 5 ft/sec, at what rate is the tip of his shadow moving?
6. A water tank in the form of an inverted cone is being emptied at the rate of 6 cubic meters per min.
The altitude of the cone is 24 m and the radius is 12 m. Find how fast the water level is lowering when
the water is 10 m deep.
7. An automobile traveling at a rate of 30 ft/sec is approaching an intersection. When the automobile is
120 ft from the intersection, a truck traveling at the rate of 40 ft/sec crosses the intersection. The
automobile and the truck are on roads that are at right angles to each other. How fast are the automobile
and the truck separating 2 sec after the truck leaves the intersection?
8. An airplane is flying at a constant speed at an altitude of 10,000 ft on a line that will take it directly
over an observer on the ground. At a given instant the observer notices that the angle of elevation of the
airplane is at 60 degrees and is increasing at a rate of 1 degree per second. Find the speed of the
airplane. (Hint - convert degrees to radians).
9. Given
3
2
x − y = 3 y−10 If dy/dt = 4 when y = 3, find dx/dt.
10. An upward facing right circular cone is being filled with water at a rate of of 48π cubic feet per
minute. If the radius r of the water in the cone is always equals its height h, then how quickly is the
1 2
radius r of the water changing when r = 4. Note: The volume of a cone is V = π r h
3