Q:

How many toothpicks can be made from a log that is 20 ft long x 3ft in diameter?

This question is from my Intro to Engineering Design class and the only math perquisite for the class is Algebra.  I'm in calculus 2 right now, so I could be over thinking the simplicity of this problem. 
How many toothpicks can be made from a log that is 20 feet long and 3 feet in diameter?  You will have to do some research or investigation for this problem.
So I found that the average toothpick has the following dimensions: 3" x 1/16"
Since no cross-sectional area is involved using calculus, I just figured I'd use the basic $\pi r^2h$
So I assumed the following:
Volume of the log: $\pi(1.5)^2(3) = 141.37$ sq/ft
Volume of the toothpick: $\pi(.03125)^2(3) = .009204$ sq/in
I then converted the square/inch of the toothpick to square/feet and got $6.39166667E-5$
Am proceeding with this correctly?  I honestly was never really good at word problems and I'm just wondering if I'm on the right track.  

A:

Volume of the log in cubic inches: $\pi(18)^2(240) = x$ cubic inches.
Volume of the toothpick: $\pi(\tfrac{1}{32})^2(3) = y$ cubic inches.
So number of toothpicks $= x/y =$ some huge number.
But, since you an engineer, you have to think about reality. The calculation above isn't really correct, because toothpicks are round, so there will be some wasted wood. For extra credit, you should consider this.
Also, toothpicks are pointed, so you could overlap their tips. For extra extra credit, consider this, too.
But, the overlapping scheme would make the manufacturing much more complex, which would increase the cost per toothpick. Again, since you are engineer, your real job is to maximize profit, not to maximize the number of toothpicks, so, for extra extra extra credit, consider whether the overlapping idea is actually a good one. 
On the other hand, the overlapping idea would save wood, even though it might reduce profits. As an environmentally responsible engineer, you should consider this, too.
Finally, as an engineer, you might consider whether a 20 foot log should be used to make toothpicks. Surely there are better uses for such a large piece of timber, whereas toothpicks can be made from any old junk little pieces.
The moral of the story (and perhaps the point of the question, if your prof is a good one) is this: engineering is much more than just mathematics; the mathematics is the easy part.

