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Related Rates

This section of AP Calculus focuses on finding rates of change for related variables, such as the volume and area of shapes, as well as the speed of objects. Explore various scenarios and learn how to apply the related rates concept.

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Related Rates

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  1. Related Rates Section 2.6 AP Calculus

  2. Find rates of two or more related variables that change with respect to time. SA Sphere: Volume Cylinder:

  3. If x and y are both differentiable functions of t, find the required value of dy/dt: Find when x=3 and =2.

  4. The radius r of a circle is increasing at a rate of 3cm/min. Find the rate of change of the area when a) r=6cm b) r=24cm

  5. The radius of a sphere is increasing at a rate of 2in/min. a) Find the rate of change of the volume when r=6 and r=24. b) Explain why the rate of change of the volume is not constant though is constant.

  6. A boat pulled into a dock by means of a winch 12 feet above the deck of the boat. a) The winch pulls in the rope at a rate of 4 ft/sec. Determine the speed of the boat when there is 13 ft of rope out. What happens to the speed as it gets closer to the dock?

  7. A boat pulled into a dock by means of a winch 12 feet above the deck of the boat. b) Suppose the boat moves at a constant rate of 4ft/sec. Determine the speed at which the winch pulls in the rope when the total rope left out is 13 ft. What happens to the speed at which the winch pulls in the rope as the boat gets closer to the dock?

  8. A fish is reeled in at a rate of 1 ft/sec from a point 10 feet above the water. At what rate is the angle between the line and the water changing when a total of 25 ft of line is still out?

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