Originally Posted by

**jgv115** The weight (W) that can be supported by a wooden beam varies directly as the square of its diameter (d) and inversely as its length (l).

a What percentage increase in the diameter would be necessary for a beam twice as long to support an equivalent weight?

What percentage change in the weight would be capable of being supported by a beam

three times as long with twice the diameter?

I know how to do this one:

$\displaystyle W \alpha \frac {d}{l} $

$\displaystyle W = \frac {kd}{l} $

$\displaystyle W = \frac {2}{3} $

So the weight needs a 33% increase.

But for this question:

What percentage increase in the diameter would be necessary for a beam twice as long to support an equivalent weight?

How do I do this?