Question

The strength of a beam varies inversely as the cube of its length. If a 12 foot beam can support 2000 pounds safely, how many pounds can a 10 foot beam support? Round to the nearest whole pound.

Answer 1

Let the strength in pounds = s
Let the beam length = x
s = k/x^3
\[s=k/x ^{3}\]
where k is a constant of proportionality
Substituting given values:
\[2000=k/12^{3}\]
\[k=2000\times 12^{3}\]
For a ten foot beam:
\[s=k/10^{3}=(2000\times 12^{3})/10^{3}\]
s = 3456 pounds

Answer 2

Thanks a lot!! ;)

Answer 3

You're welcome :)