SOLUTION: Ok, sorry but this word problem is killing me. It's not like any of the others I've done... Here it is: "It is shown in engineering that the maximum load a cylindrical column

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Question 158845: Ok, sorry but this word problem is killing me. It's not like any of the others I've done... Here it is:
"It is shown in engineering that the maximum load a cylindrical column of circular cross-section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. If a column 16 feet high and 4 feet in diameter will support a load of 10 tons, how great a load will be supported by a column 20 feet high and 6 feet in diameter?"
Thanks!
Josh
Found 3 solutions by scott8148, stanbon, Earlsdon:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
L=kd^4/h^2 __ 10=k*4^4/16^2 __ 10=k

L=10*6^4/20^2 __ L=32.4

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
It is shown in engineering that the maximum load a cylindrical column of circular cross-section can hold varies directly as the fourth power of the diameter and inversely as the square of the height.
load = k * d^4/h^2
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If a column 16 feet high and 4 feet in diameter will support a load of 10 tons,
Find "k":
10 = k * 4^4/16^2
10 = k * 1
k = 10
--------------
Equation now that we know k = 10:
load = 10 * d^4/h^2
--------------
how great a load will be supported by a column 20 feet high and 6 feet in diameter?
load = 10 * 6^4/20^2
load = 32.4 tons
===========================
Cheers,
Stan H.

Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website!
First, write the equation of variation:
Where: L = load, d = diameter, h = height, and k = the constant of variation.
You need to find the value of k first, so substitute the given values of L (10 tons), d (4 feet), and h (16 feet).

Now you can answer the question:

tons.