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 \textit{\underline{V} varies jointly with \underline{B} and \underline{h}}\qquad V=kBh
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\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
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\cfrac{1}{3}=k\qquad therefore\qquad \boxed{V=\cfrac{1}{3}Bh}
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\textit{when h = 12, and V = 124, what is \underline{B}?}\qquad 124=\cfrac{1}{3}B(12)[/tex]