Question

10m3 of air weigh 13 kg. The weight of air is directly proportional to its volume. Find the constant of variation; it is called density

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{weight of air is directly proportional to its volume}\qquad W=kV \\\\\\ \textit{we also know that } \begin{cases} V=10\\ W=13 \end{cases}\implies 13=k10\implies \cfrac{13}{10}=k$