## How big is Mega Maid’s vacuum bag; “Spaceballs”

Artifact

Scene from Mel Brooks’ classic, Spaceballs. Start off by simply showing it (or any combination of the split scenes) to your students (apologies if there are advertisements, you can skip them in like 5 seconds):

Now, I’m not sure if you’d want to show the entire scene in a classroom setting, both because it’s rather long and because there are some, *ahem* cruder moments (“sir, she’s gone from suck to blow“). Personally, I think starting off the first five minutes of class with the entire scene might engage the kids, make them laugh, wake up, etc. But then, I don’t have any administrators or parents to answer to at the moment. Regardless, I’ve broken up the scene into five pieces, which I share below.

Guiding Questions (GQs)

Personally, this scene brings up a ton of questions for myself. Hopefully after watching the scene there will be several GQs from your students. Here are the two primary GQs (a.k.a. “Need to Knows” for you PBL types) that will lead to the mathematics behind this scene that I have.

• How much air is in Planet Druidia?
• How big is Planet Druidia?
• How far above the surface is the “air shield”?
• How quickly can Mega Maid suck the air out of a planet?
• Did Mega Maid blow out the air faster than she sucked it in?

Solutions to GQs

Here is Planet Druidia again.

The two questions we really can’t answer for certain are “how big is Druidia?” and “how far above the surface is the ‘air shield’?”. But, you know what? Planet Druidia looks a lot like Earth to me, so let’s run with that.

What we need to find for the volume of air is the volume of a spherical shell. Or, the volume of two concentric spheres of differing radii.

So for this particular problem, we have

or,