Question 1029013
Use the disk method.


Integrate in y from y = 1 to y = 27 (the graphs of *[tex \large x = 3] and *[tex \large y = x^3] intersect at (3,27). For a given y, the radius of each cross-section is *[tex \large 3 - \sqrt[3]{y}] (it's easier to draw it out). Then the volume is equal to the integral


*[tex \large V = \int_{1}^{27} \pi (3 - \sqrt[3]{y})^2 \mathrm{d}y]