Friday, December 11, 2009
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.
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!
Posted by Excelmathmike at 8:58 AM