
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?
The radius of the cylinder. The height of the cylinder. The surface area of the cylinder. The volume of the cylinder.
In the context above, which of the following should be assumed to be constant?
The radius of the cylinder. The height of the cylinder. The surface area of the cylinder. The volume of the cylinder.