We solve related rates problems in context.

Now we are ready to solve related rates problems in context. Just as before, we are going to follow essentially the same plan of attack in each problem.
Introduce variables, identify the given rate and the unknown rate.
Assign a variable to each quantity that changes in time.
Draw a picture.
If possible, draw a schematic picture with all the relevant information.
Find equations.
Write equations that relate all relevant variables.
Differentiate with respect to t.
Here we will often use implicit differentiation and obtain an equation that relates the given rate and the unknown rate.
Evaluate and solve.
Evaluate each quantity at the relevant instant and solve for the unknown rate.

Formulas

In our next problem, we will stretch and flatten a cylinder-shaped pizza dough.

In our next example we consider a melting snowball.

Right triangles

Angular rates

Similar triangles