Final answer:
To solve the equation for z when x=8 and y=6, we can use the concept of direct and inverse variation, substituting the given values into the equation and solving for the constant of variation, k. Then we can plug in the values of x=8 and y=6 to find the value of z.
Step-by-step explanation:
To find the value of z when x=8 and y=6, we can use the concept of direct and inverse variation. The given equation is z varies directly as x^3 and inversely as y^3, which can be written as z=kx^3/y^3, where k is the constant of variation.
Using the given values z=61, x=6, and y=9, we can substitute these values into the equation and solve for k. 61=k*6^3/9^3. Solving this equation, we find k=1.5.
Now, we can use this value of k to find z when x=8 and y=6. Substituting these values into the equation, we get z=1.5*8^3/6^3. Evaluating this expression, we find z≈11.52.