Let's assume you got behind on your
firewood splitting and needed to purchase some firewood for a week
till you get caught up. You check you local paper and see they have
prices of $80 per truck-load. What can one expect from a truck-load
of wood? How many units? How much is this per unit? We will be using
some basic volume to get the number of units and use this number to
get a per unit price. We could then decide how long it will last
based on types of wood, etc (Note: The purpose of this activity is for the application more so than for the usefulness. As anyone whose ever split wood knows, quality has more to do with density and how well the wood is seasoned..see below)

__Measurements Used__

Full Size F-150 Long-bed Truck

Length = 8ft

Width = 6.5ft

Height = 1.6ft

Piece of Firewood (We will assume the
average log length is 18inches and has a radius of 8 inches which
will be cut into 8 pieces for firewood)

__Units of Firewood by Volume__

For the sake of ease, let us assume
that a truckload of firewood will be neatly stacked but not higher
than the sides of the truck.

**Volume of truck bed**

8x6.5x1.6 = 83.2ft^3

**Volume of Firewood Log**

Changing Our Units to feet

length = 18 inches = 1.5ft

radius = 8 inches = 0.66ft

Volume of a cylinder equals

V = (pi)(r^2)(h)

V = (3.14)(0.44)(1.5) = 2.05ft^3

**Volume of Firewood Piece (once split into 8 pieces)**

2.05ft^3 / 8 =
0.26ft^3

__Units of Firewood Per Truckload__

Now that we know the volume of both the
truck-bed and for a piece of fire wood we can simply divide them to
see how much firewood should stack neatly into the truck-bed

83.2 / 0.26 = 320 pieces of firewood

__Adjusting For The Odd Shapes__

Since the pieces of firewood are not
cubic, they are circle-sections. They will not stack neatly together.
There will be added spacing between them. The seller could compensate
for this by stacking the firewood above the walls of their truck, but
we will assume they didn't.

This spacing could be compensated with
a little optimization. But, from stacking wood I think it would be
safe to say that four every 10 pieces you will loose one to spacing.
Thus we will loose 1/10th of our total to spacing. 1/10 of 320 = 32

320 – 32 = 288pieces of firewood.

__Prices Per Unit__

At the rate of $80 per truck-load. We
have $80 per 288 pieces of wood

80/288 = $0.28 per unit.

__The Calculations Are Quite Arbitrary__

These
calculations are quite arbitrary in their usefulness. Most firewood
comes in different sizes. A true calculation of how good the deal on
firewood would to compare volume to density as well as how seasoned.
The purpose of this posting was simply to serve as an application.

__From Here We Could__

From
here we could ask questions like.

1) If
we use 40 pieces of firewood per night, how long will this last us?

2) If you wanted to, you could make a
step-function based on how cold it is outside.

At 40 degrees we use 10 pieces of
firewood per night

At 30 degrees we use 30 pieces of
firewood per night

etc.

3) Could recalculate based on the volume questions for different size truck-beds or different materials

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