1. The problem is to find the volume of a solid of revolution using the cylindrical shell method. 2. Suppose we revolve the region bounded by a function $y=f(x)$, the x-axis, and vertical lines $x=a$ and $x=b$ around the y-axis. 3. The volume $V$ is given by the integral formula using cylindrical shells: $$V = 2\pi \int_a^b x f(x) \, dx$$ 4. Here, $x$ is the radius of the shell, $f(x)$ is the height, and $2\pi x$ is the circumference. 5. To apply, identify $f(x)$, $a$, and $b$ from the problem, then compute the integral. 6. Evaluate the integral to find the volume. This method is especially useful when revolving around the y-axis and the function is given in terms of $x$.