Question

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 of 14 metric tons. How many metric tons will be supported by a column 8 m high and two thirds m in​ diameter?

Answer 1

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

$L=\dfrac{kd^4}{h^2}\\\\14=\dfrac{1.k}{9^2}\\\\14\times 81=k\\\\k=1134$

If the height of columns = 8 m

Diameter = $\dfrac{2}{3}\ m$

So, Load would be

$L=\dfrac{1134\times (\dfrac{2}{3})^4}{8^2}\\\\L=3.5\ tons$

Hence, there are 3.5 metric tons will be supported by a column 8 m high and two thirds m in diameter.