Precalc

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 ________________.

1. V=(1/3)πr(kr^2/3)
2. V=(1/3)πkr^3
3. V=(1/3)πkr^8/3
4. V=(1/3)πr^2

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  1. well, shucks -- just plug it in

    (1/3)πr^2h = (1/3)πr^2*(kr^2/3) = (1/3)πk r^8/3

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