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?
:
L = {{{(kd^4)/h^2}}}; 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 = {{{(1^4*k)/9^2}}}
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 = {{{(.6667^4*1215)/8^2}}}
L = {{{(.19757*1215)/64}}}
L = 3.75 tons max load