SOLUTION: Hello. My husband and I are trying to figure out how many cord of wood we have just split. It's piled into a cone area with a base area of 19' across and 8' high. Approximately

Algebra ->  Formulas -> SOLUTION: Hello. My husband and I are trying to figure out how many cord of wood we have just split. It's piled into a cone area with a base area of 19' across and 8' high. Approximately      Log On


   

Question 189566: Hello. My husband and I are trying to figure out how many cord of wood we have just split. It's piled into a cone area with a base area of 19' across and 8' high. Approximately how many cord do we have???
Thank you,
Joanna
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: a cord of wood is defined to be 4 feet high by 4 feet wide by 8 feet long which gives a volume of 4%2A4%2A8=128 cubic feet.


I'm assuming that the cone has a base diameter of 19'. Or is the base area 19 square feet? If the base has a diameter of 19', this would then mean that the base radius is 9.5'. So r=9.5 (if the assumption is correct).


What you want to do first is find the volume of the cone


V=%281%2F3%29pi%2Ar%5E2%2Ah Start with the volume of a cone equation.


V=%281%2F3%29%283.14%29%289.5%29%5E2%288%29 Plug in r=9.5 and h=8. Also, replace pi with 3.14


V=%281%2F3%29%283.14%29%2890.25%29%288%29 Square 9.5 to get 90.25


V=2267.08%2F3 Multiply


V=755.693 Divide


So the volume of the cone is approximately 755.693 cubic feet.


Now take the volume of the cone and divide it into the volume of one cord of wood to get

755.693%2F128=5.904


So there are about 5 full cords (almost 6) of wood in that pile.