SOLUTION: A lumber company needs to estimate the volume of wood a load of timber will produce.The supervisor knows that the volume of wood in a tree varies jointly as the height h and the sq

Click here to see ALL problems on Probability-and-statistics

Question 548865: A lumber company needs to estimate the volume of wood a load of timber will produce.The supervisor knows that the volume of wood in a tree varies jointly as the height h and the square of the tree's girth g.The supervisor observes that a tree 40 meters tall with a girth of 1.5 meters produces 288 cubic meters of wood.
a)Write an equation that represents this situation.
b)What volume of wood can the supervisor expect to obtain from 50 trees averaging 75 meters in height and 2 meters in girth?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A lumber company needs to estimate the volume of wood a load of timber will produce. The supervisor knows that the volume of wood in a tree varies jointly as the height h and the square of the tree's girth g.
---
v = k*h*g^2
-----
Solve for "k" using "The supervisor observes that a tree 40 meters tall with a girth of 1.5 meters produces 288 cubic meters of wood."
----
288 = k*40*1.5^2
k = 288/(40*1.5^2) = 3.2
------
a)Write an equation that represents this situation.
v = 3.2*h*g^2
-------------
b)What volume of wood can the supervisor expect to obtain from 50 trees averaging 75 meters in height and 2 meters in girth?
v(1 tree) = 3.2*75*2^2 = 960 cu meters
---
v(50 trees) = 50*960 = 48000 cu meters
==========================
Cheers,
Stan H.
=============