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?

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

If the height of columns = 8 m

Diameter =

So, Load would be

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

answer: 7270

step-by-step explanation: