Answer: There are 3.5 metric tons will be supported by a column 8 m high and two thirds m in diameter.
Step-by-step explanation:
Since we have given that
Height of columns of arena = 9 m
Diameter = 1 m
Load = 14 metric tons
Since Load is directly varies as the fourth power of the diameter 'd', and inversely as the square of the height.
so, Mathematically, it is expressed as
[tex]L=\dfrac{kd^4}{h^2}\\\\14=\dfrac{1.k}{9^2}\\\\14\times 81=k\\\\k=1134[/tex]
If the height of columns = 8 m
Diameter = [tex]\dfrac{2}{3}\ m[/tex]
So, Load would be
[tex]L=\dfrac{1134\times (\dfrac{2}{3})^4}{8^2}\\\\L=3.5\ tons[/tex]
Hence, there are 3.5 metric tons will be supported by a column 8 m high and two thirds m in diameter.
