## Related Rates

### Related Rates: Problems and Solutions

We will solve every Related Rates problem using the same Problem Solving Strategy time and again. You can see an overview of that strategy here (link will open in a new tab).

As stated in the Problem Solving Strategy, nearly every Related Rates problem will fall into one of four subcategories. With practice, you’ll learn to recognize each:

Click to view Calculus solution to “Snowball melts, area decreases at given rate,” with video

An inverted cone is 20 cm tall, has an opening radius of 8 cm, and was initially full of water. The water now drains from the cone at the constant rate of 15 cm$^3$ each second. The water’s surface level falls as a result. At what rate is the water level falling when the water is halfway down the cone?

Click to view Calculus solution to “Lamp post casts a shadow of a man walking,” with video

Click to view full Calculus solution to “How fast is the ladder’s top sliding?” with video

If $y = x^3 + 2x$ and $\dfrac{dx}{dt} = 6$, find $\dfrac{dy}{dt}$ when $x=5.$

Click to view full Calculus solution to “Given an equation, find a rate.”

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