Two young mathematicians discuss tossing pizza dough.
Check out this dialogue between two calculus students (based on a true story):
- Devyn
- Hey Riley, do you know what I love?
- Riley
- Calculus?
- Devyn
- And pizza! Last night I made my own pizza crust from scratch!
- Riley
- Mmmmmmm. Calculus.
- Devyn
- I know! The best part of making the crust is tossing it. But during my pizza tossing, I noticed something. The dough is basically a cylinder with a radius that is expanding, and a height that is getting smaller. Then I started wondering: how are those two rates related?
- Riley
- Pizza. So delicious. So cheesy. So calculus.
The problem above is an example of a related rates word problem. To solve it, we will need the tools in the Dig-In. For now, let’s see if we can reason through some questions related to this problem.
In the context above, which of the following should be assumed to be
functions that vary?