Question 1120501: The volume of wood, V, obtained from a tree varies jointly as the height, h, and the square of the girth (the distance around the tree trunk), g. if the volume is 38.4ft^3 when the height is 30 ft and the girth is 4ft, what is the volume when the height is 50 ft and the girth is 7 ft?
a. 198.35 ft^3
b.196 ft^3
c.199 ft^3
d.191.76 ft^3
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39626)   (Show Source):
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The other tutor showed a partial solution using the formal definition of joint variation, finding the value of the constant of proportionality using the given measurements and then using that constant with the new measurements to get the new volume.
That of course is a valid method for solving the problem. And if you had several other trees with different measurements, you would probably want to use that method, since it would give you a formula you could use repeatedly for each set of measurements.
But when you are only asked to find the volume of one other tree, I find it much easier just to multiply the given volume by the ratios of the new measurements to the old.
In this example, the second tree is 5/3 the height of the first (50 ft vs. 30 ft); the girth is 7/4 as much (7 ft vs. 4 ft). Since the volume varies jointly as the height and the square of the girth, the volume of the second tree is
Answer: b. 196 cubic feet
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