The quantity y varies directly with the square of x and inversely with z. when x is 9 and z is 27, y is 6. what is the constant of variation?

Yvaires directly as x means
y=kx

y varies inversly with z means
y=k/z

therfor
y=(kx^2)/z
k=constant of variation

6=(k9^2)/27
6=(k81)/27
6=3k
divide both sides by 3
2=k

the constant of variation is 2

Are you trying to figure out the volume?