Could you live here?

I read an article today about the smallest condo-apartment in New York City. A married couple and two cats live in this space. I've created a floor plan with a bed and two chairs.

In Excel Math we ask students to cut out furniture shapes and arrange them on a floor plan, to use their geometry and measuring skills. In a later set of lessons, we ask them to calculate the cubic volume of a houseful of furniture. That's helpful in choosing a moving van, or deciding how much you can take to a college dorm room (this helps avoid fights with your new roommate!).

Here's the lesson content, re-arranged for the blog. Julio's dad asked him to calculate how large a truck they would need for this set of furniture.

Our math questions are these:

1. Can we fit all the furniture into the apartment?
2. If so, how high is the pile going to be?

Assumptions: there's no furniture to start with, the kitchen cabinets stay, you can't use the bathroom space, and the ceilings are 8 feet high.


I estimate that the kitchen cabinets are 2 feet by 7 feet. That's 2 x 7 x 8 = 112 cubic feet.
The main room is 10 x 15 x 8 = 1200 cubic feet. Subtract 112 and we have 1088 cubic feet.
The door still has to be opened and closed, so we have to take off about 3 x 3 x 8 or 72 cubic feet.
We'll round to 1000 cubic feet.

We only have to fit in 440 cubic feet of stuff.
The apartment will be 440/1000s full. We can simplify that to 44/100ths or 22/50, 11/25.
That's about 44%.
The depth of the pile will be 96 inches x .44 = 42 inches deep.
We will have 3 1/2 feet of stuff across every square inch of the room.

Anyone who's ever packed a moving van knows these numbers mean very little. There's always air space and you never pack everything with 100% efficiency.

Add some clothing, a few cushions and I predict the room will be filled to the ceiling!