SOLUTION: the roof of a new sports arena rests on round concrete pillars. THe maximum load a cylindrical column of a circular cross section can hold varies directly as the fourth power of th

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Question 978957: the roof of a new sports arena rests on round concrete pillars. THe maximum load a cylindrical column of a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. The arena has 9 m tall columns that are 1 m in diameter and will support a load 15 metric tons. How many metric tons will be supported by a column 8m high and 2/3 m in diameter?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the roof of a new sports arena rests on round concrete pillars.
THe maximum load a cylindrical column of a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height.
The arena has 9 m tall columns that are 1 m in diameter and will support a load 15 metric tons.
How many metric tons will be supported by a column 8m high and 2/3 m in diameter?
:
L = %28kd%5E4%29%2Fh%5E2; where
L = max load
k = constant of variation
d = diameter of the pillar
h = the height
"The arena has 9 m tall columns that are 1 m in diameter and will support a load 15 metric tons."
15 = %281%5E4%2Ak%29%2F9%5E2
81*15 = k
k = 1215 is the constant
:
"How many metric tons will be supported by a column 8m high and 2/3 m in diameter?
use .6667 for 2/3 meter
L = %28.6667%5E4%2A1215%29%2F8%5E2
L = %28.19757%2A1215%29%2F64
L = 3.75 tons max load