AP Calculus AB: Related Rates — Drill 1

About This Drill

AP Calculus AB: Related Rates — Drill 1 is a Math practice drill covering Related Rates. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice setting up and solving related rates problems involving expanding circles, expanding spheres, a sliding ladder, and a filling conical tank. These AP Calculus AB problems require applying the chain rule to equations relating two or more changing quantities.

Questions in This Drill

1. The radius of a circle is increasing at a constant rate of 3 cm/sec. At the instant when the radius is 5 cm, what is the rate at which the area of the circle is increasing?
2. The volume of a sphere is increasing at a rate of \( 16\pi \) in³/sec. At the instant when the radius is 2 inches, what is the rate at which the radius is increasing?
3. A 10-foot ladder leans against a vertical wall. The base of the ladder slides away from the wall at 2 ft/sec. At the instant when the base is 6 feet from the wall, at what rate is the top of the ladder sliding down the wall?
4. Water is poured into an inverted conical tank at 2 ft³/min. The tank has a height of 10 ft and a base radius of 5 ft. At the instant when the water is 4 ft deep, at what rate is the water level rising?
5. A streetlight is mounted at the top of a 15-foot pole. A person 6 feet tall walks away from the base of the pole at 4 ft/sec along a straight path. At what rate is the tip of the person's shadow moving away from the base of the pole?