Related Rates Practice Worksheet
A Grade 10 Calculus worksheet on related rates, covering problems involving geometry and motion.
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Related Rates Practice Worksheet
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Read each problem carefully and solve for the requested related rate. Show all your work and include units in your final answers.
1. A ladder 10 meters long is leaning against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.2 m/s, how fast is the top of the ladder sliding down the wall when the bottom is 6 meters from the wall?
2. The radius of a circle is increasing at a rate of 2 cm/s. How fast is the area of the circle increasing when the radius is 5 cm?
Given: dr/dt = cm/s
Formula for Area of a circle: A =
Differentiate with respect to time (t): dA/dt =
Substitute r = 5 cm: dA/dt = cm²/s
3. Water is being poured into a conical tank at a rate of 8 cubic feet per minute. The tank is 20 feet high and has a radius of 10 feet. How fast is the water level rising when the water is 12 feet deep?
4. A man 6 feet tall walks away from a lamppost that is 15 feet high. If he walks at a speed of 4 ft/s, how fast is the tip of his shadow moving when he is 10 feet from the lamppost?
20/3 ft/s
10/3 ft/s
8/3 ft/s
4 ft/s
5. A particle moves along the curve y = √(x). Find the rate of change of the distance between the particle and the origin when x = 4, given that dx/dt = 3 cm/s.