# Extra Practice Related Ratesap Calculus

This video lesson explores the concept of Related Rates, which is the study of what is happening over time.

• Math AP®︎/College Calculus AB Contextual applications of differentiation Solving related rates problems Solving related rates problems Practice: Related rates intro.
• To solve problems with Related Rates, we will need to know how to differentiate implicitly, as most problems will be formulas of one or more variables. But this time we are going to take the derivative with respect to time, t, so this means we will multiply by a differential for the derivative of every variable!

To solve problems with Related Rates, we will need to know how to differentiate implicitly, as most problems will be formulas of one or more variables.

But this time we are going to take the derivative with respect to time, t, so this means we will multiply by a differential for the derivative of every variable!

But don’t let this confused you, as there are only four basic steps when problem-solving with Related Rates:

Section 3-11: Related Rates. In this section we are going to look at an application of implicit differentiation. Most of the applications of derivatives are in the next chapter however there are a couple of reasons for placing it in this chapter as opposed to putting it into the next chapter with the other applications.

1. Write down every given information or quantity, even what you’re looking for, and make a sketch.
2. Determine the equation needed to solve for your unknown quantity.
3. Take the derivative implicitly, not forgetting to multiply by your differential for every single variable!
4. Plug in all of your given information or quantities and solve.

And here’s a big hint…

…most of the time all we have to do is find an equation that relates the rate we’re looking for to a rate that we already know, as Paul’s Online Notes so nicely states.

This means we need to look for geometric shapes, known formulas, and ratios.

Together we will solve these 8 classic questions:

• Pebble Dropped In Pond
• Air Being Pumped Into A Balloon
• Edges Of Cube Expanding
• Radar Tracking Station & Airplane Flight Path
• Sand Falling onto a Conical Pile
• Water Pouring into a Conical Tank
• Boat Pulled into a Dock
• Ladder Sliding Down a Wall

## How to Solve Related Rates – Video

1 hr 35 min

• Overview of Related Rates + Tips to Solve Them
• 00:02:58 – Increasing Area of a Circle
• 00:12:30 – Expanding Volume of a Sphere
• 00:21:15 – Expanding Volume of a Cube
• 00:26:32 – Calculate the Speed of an Airplane
• 00:39:13 – Conical Sand Pile
• 00:51:19 – Conical Water Tank
• 00:59:59 – Boat & Winch
• 01:09:13 – Ladder Sliding Down A Wall

## Related Rates

Related Rates – 2 Examples