Related Rates Worksheet
This worksheet focuses on related rates problems in Calculus, covering various geometric shapes and real-world scenarios.
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Related Rates Worksheet
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Read each problem carefully and solve for the requested related rate. Show all your work.
1. A spherical balloon is being inflated. If the radius is increasing at a rate of 2 cm/s, how fast is the volume increasing when the radius is 10 cm?
2. A 13-foot ladder is leaning against a wall. If the top of the ladder is sliding down the wall at a rate of 0.5 ft/s, how fast is the bottom of the ladder moving away from the wall when the top is 5 feet from the ground?
3. Water is being poured into a conical tank at a rate of 5 cubic feet per minute. The tank is 20 feet tall and has a radius of 10 feet. How fast is the water level rising when the water is 8 feet deep?
4. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock 10 feet higher than the bow of the boat. If the rope is pulled in at a rate of 2 ft/s, how fast is the boat approaching the dock when 26 feet of rope are out?
5. Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. What is the rate of change of the radius when the radius is 3 feet?
0.04 ft/min
0.08 ft/min
0.12 ft/min
0.16 ft/min
6. A cylindrical tank with a radius of 5 meters is being filled with water at a rate of 3 cubic meters per minute. How fast is the height of the water increasing?