Question

The maximum load that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. A 9 meter column 2 meters in diameter will support 64 metric tons. How many metric tons can be supported by a column 9 meters high and 3 meters in diameter?

• A. $342$ metric tons
• B. $524$ metric tons
• C. $324$ metric tons
• D. None of these

Answer 1

The correct option is C $324$ metric tons

Let the given Function be represented as

$Load\left(L\right)=k(\frac{d^4}{h^2})$

Let us find the Value of $k$

$\Rightarrow 64=k\frac{16}{81}$

$\Rightarrow k=324$

Now Let us use the Above Formula for $h=9$ and $d=3$

$Load=324\times \frac{81}{81}$

$Load=324$

Therefore Answer is $\left(C\right)$