precalc

posted by .

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

  • precalc -

    taking your formulas at face value and guessing that
    the strange symbol is supposed to be π,
    sub h = kr^2/3 into V = (1/3)πr^2h
    to get
    V = (1/3)πr^2(kr^2/3)
    = (1/9)kr^4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra1

    M varies directly with n; m=144 when n=8. What is the constant of variation k?
  2. calc - question #1

    A frustum of a right circular cone with height h, lower base radius R, and top radius r. -what's the volume using h, R, & r in the answer?
  3. Math

    DIRECT VARIATION 1. a is directly proportional to b.If a=15,then b=9 2. m varies directly as n.If n=2/3,then m=1/4 3. T varies as the square root of L. If L=81,then T=10 4.r varies directly as the square of t. If t=16,then r=6. 5. …
  4. Intermediate Algebra

    a male born in 1975 does not want his future wife to outlive him. What should be the year of birth for his wife so that they both can be expected to die in the same year?
  5. MLA format English

    . An article accessed through a library data base by May Gottchalk titled Reconsidering Dyslexia. The article was published in the May 24, 2002, issue of Education Matters and you retrieved the article using Wilson Select on November …
  6. Math

    The time needed to empty a vertical cylindrical tank varies directly as the square root of the height of the tank and the square of its radius. By what factor will the emptying time change if the height is doubled and the radius increased …
  7. math

    t varies directly as the square root of l. If l=81, then t=10 what is the constant proportion?
  8. Math

    The volume of a cylinder is given by formula V= pi(3.14) r^2h where r is base radius and h is height a) the height of a cylinder of radius 5cm and volume 500. Cm^3 B) radius of base of a cylinder of volume 300 cm^3 and height 10 cm …
  9. Pre-Calc

    1.) Suppose that y varies directly as x. If y is 5 when x is 30, the constant of variation is 150. True Or False 2.) If w varies directly as z and w = 9 when z = -6, find w when z = 3. 3.) If y varies directly as x and y = 2 when x …
  10. Algebra

    The volume of a right circular cylinder (think of a pop can) is jointly proportional to the square of the radius of the circular base and to the height. For example, when the height is 10.62 cm and the radius is 3 cm, then the volume …

More Similar Questions