Cord of wood

[johnr]

Does it really matter, either you buy the wood or you don't.

My thoughts too

 

[Davy Crockett]

My guess is that Lunk is dickering on some logs to mill into lumber and crunching numbers with the owner. The owner asked what is the cut and split price of those logs so lunker asked us.

 

[lunkerslayer]

Yes my neighbor has like 20 dead oak and ash trees in his horse pen that he is taking down, hes got them cut into 9 foot logs already and just wanted to know since ive never bought wood for the business since i have a gasification wood boiler stove. Dad bought wood from a few local tree services who got paid to take trees down and would then sell the wood to him at a discount price. But all this wood is already dead and would be great since i can only burn wood that has less the 25 percent moisture.

 

[Wall-eyes]

What you're solving for


You are determining the fraction of a cord of wood represented by a single log with specific dimensions.


What's given in the problem

• The log is round with a diameter of
  
  
  
  12 inches12 inches
  .
• The log is
  
  
  
  9 feet9 feet
  tall.
• A cord of wood is defined as
  
  
  
  128 cubic feet128 cubic feet
  .
  
  
  
  

Helpful information

• The volume of a cylinder is calculated using the formula
  
  
  
  V=πr2hcap V equals pi r squared h
  .
• A cord of wood accounts for air space between logs, so the solid wood volume will be less than the total cord volume.
  
  

How to solve


Calculate the volume of the log and then determine its proportion relative to a cord of wood, accounting for air space.

1. 
   Step 1 . Convert the log's diameter to feet and calculate its radius.
   
   • Diameter in feet:
     
     
     
     D=12 inches12 inches/foot=1 footcap D equals the fraction with numerator 12 inches and denominator 12 inches/foot end-fraction equals 1 foot
     .
   • Radius in feet:
     
     
     
     r=D2=1 foot2=0.5 feetr equals the fraction with numerator cap D and denominator 2 end-fraction equals the fraction with numerator 1 foot and denominator 2 end-fraction equals 0.5 feet
     .
   
   Step 2 . Calculate the volume of the log in cubic feet.
   
   • Volume of log:
     
     
     
     Vlog=πr2hcap V sub log end-sub equals pi r squared h
     .
   • 
     
     Vlog=π×(0.5 feet)2×9 feetcap V sub log end-sub equals pi cross open paren 0.5 feet close paren squared cross 9 feet
     .
   • 
     
     Vlog=π×0.25 feet2×9 feet≈7.068 cubic feetcap V sub log end-sub equals pi cross 0.25 feet squared cross 9 feet is approximately equal to 7.068 cubic feet
     .
   
   Step 3 . Estimate the solid wood volume within a cord.
   
   • Assume solid wood occupies about
     
     
     
     80%80 %
     of a cord's volume due to air space.
   • Solid wood volume in a cord:
     
     
     
     Vsolid cord=128 cubic feet×0.80=102.4 cubic feetcap V sub solid cord end-sub equals 128 cubic feet cross 0.80 equals 102.4 cubic feet
     .
   
   Step 4 . Determine how close the log is to a cord of wood.
   
   • Fraction of a cord:
     
     
     
     Fraction=VlogVsolid cordFraction equals the fraction with numerator cap V sub log end-sub and denominator cap V sub solid cord end-sub end-fraction
     .
   • 
     
     Fraction=7.068 cubic feet102.4 cubic feet≈0.069Fraction equals the fraction with numerator 7.068 cubic feet and denominator 102.4 cubic feet end-fraction is approximately equal to 0.069
     .

Solution


A single

12 inch12 inch
diameter,

9 foot9 foot
tall log is approximately

0.0690.069
of a cord of wood.

 

[svnmag]