Posted by **Anonymous** on Friday, August 27, 2010 at 12:13am.

According to an article by Thomas H. McMahon in the July 1975 issue of Scientific American, a tree’s height varies directly with the radius of the base of its trunk. He expressed this relation using the formula h = kr^2/3 where k is a constant, h is the tree’s height, and r is the tree’s radius.

Now suppose you own a stand of trees whose pulp can be used for making paper. The amount of wood pulp you can produce from a tree increases as the tree’s volume increases. The model approximates a tree without its branches as a right circular cone. The formula for the volume of the tree then becomes V = (1/3)πr^2h.

Substituting the formula for height of a tree in the formula for volume of a tree, the new formula for volume becomes

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