A hint to get started
Choose the outer radius after rewriting in terms of y
Find the value of the volume of the solid formed by rotating the region between and about the y-axis.
CJC · Lecture · Example 18
The Teacher supplies the otherwise blank sketch/working, labels the rewritten cubic root as f(y) and square root as g(y), and fills the difference-of-squares integral. All are integrated into the radius comparison and reconstructed figure.
The final Teacher summary distinguishes x-axis y²dx, y-axis x²dy and translated axes; retain the matching variable, bounds and radius in each setup.