Practice Related Rates in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Problems where two or more quantities change with time and are related by an equation. Differentiate the equation with respect to time t and use known rates to find an unknown rate.
If two quantities are linked by an equation, their rates of change are also linked. A balloon inflating: as the radius increases, the volume increases too. How fast does the volume grow if the radius grows at 2 cm/s? The chain rule connects the rates.
Example 1
easyA spherical balloon is being inflated so its radius increases at 2 cm/s. How fast is the volume increasing when the radius is 5 cm?
Example 2
hardA 13-ft ladder rests against a wall. The base slides away at 5 ft/s. How fast is the top sliding down when the base is 5 ft from the wall?
Example 3
easyA circle's radius grows at 3 cm/s. How fast is the area increasing when r = 10 cm?
Example 4
mediumWater fills a cone (apex down) of radius 3 m and height 6 m at 2 m³/min. How fast is the water level rising when h = 4 m?