Answer :
The constant of variation is 1/6 and variation equation is y=(1/6)*[tex]x^{3}[/tex] .
This is a question of direct variation .
⇒ y is directly proportional to x .
Since y varies directly as the cube of x .
Let k be the constant of variation .
y = k[tex]x^{3}[/tex] eq1
Substituting values of y and x in the above quadratic equation
36 = k[tex]6^{3}[/tex]
k = 36/216
k= 1/6
Hence , constant of variation = 1/6 .
Variation Equation is made by substituting value of Constant of Variation in above equation .
Variation equation is
y=(1/6)*[tex]x^{3}[/tex]
Therefore , constant of variation = 1/6 and variation equation is
y=(1/6)*[tex]x^{3}[/tex] .
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