Given that
Y is inversely proportional to the cube of x. If Y = 6 when x = 2, then the constant of variation is 48.
Explanation -
The given condition can be represented as
[tex]\begin{gathered} Y\propto\frac{1}{x^3} \\ Y=k\times\frac{1}{x^3} \\ where\text{ k = constant variation} \end{gathered}[/tex]By substituting values we get
[tex]\begin{gathered} 6=k\times\frac{1}{2^3} \\ 6=k\times\frac{1}{8} \\ k=6\times8=48 \\ k=48 \end{gathered}[/tex]So the final answer is 48.
Final answer -
Hence the final answer is 48. So, it is true.