tricky math

Yikes--I was just reviewing the math lesson that I'm supposed to use next week with my kids, and one of the problems can be summed up as:

We have two proposed building designs. Both are 600 feet tall, and one is a cylinder with a radius of 40 feet and the other is a rectangular design with sides of 75 and 85 feet. Which one will hold more people? The kids calculate surface area and volume:

Cylinder
SA: 160,850 sq. ft.
V: 3,015,929 cu. ft.

Rectangular solid
SA: 204,750 sq. ft.
V: 3,825,000 cu. ft.

The lesson then concludes that "although the buildings seem to be about the same size, there are big differences between the area inside." Okay, true enough for the dimensions given, although it's not really a fair comparison, but maybe there's going to be a valid point in here somewhere... and then this is the final word on the subject: "This is one reason we tend to see many buildings like the rectangular prism, and fewer like the cylinder."

In other news, I had a bowl of oatmeal for breakfast and an apple for lunch. This is one reason why breakfast tends to be more filling than lunch.