The volume of a cone varies jointly with the area of the base and the height. When the area of the base is 27 cm2 and the height is 6 cm, the volume is 54 cm3. Therefore, the area of the base is _____ cm2 when the height is 12 cm and the volume is 124 cm3.

[tex]\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}\\\\ -------------------------------[/tex]

[tex]\bf \textit{\underline{V} varies jointly with \underline{B} and \underline{h}}\qquad V=kBh \\\\\\ \textit{we also know that } \begin{cases} B=27\\ h=6\\ V=54 \end{cases}\implies 54=k(27)(6)\implies \cfrac{54}{(27)(6)}=k \\\\\\ \cfrac{1}{3}=k\qquad therefore\qquad \boxed{V=\cfrac{1}{3}Bh} \\\\\\ \textit{when h = 12, and V = 124, what is \underline{B}?}\qquad 124=\cfrac{1}{3}B(12)[/tex]