Calculate the volume of the cone and cylinder. calculate the volume of the shaded region.

Notice the picture above, the cone, is inside the cylinder

now, the cylinder has a height of h = 9, and radius of r = 3
so its volume is    

now, what's the height of the cone? well, the cone is snug-fit inside the cylinder, so, it has a height of h = 9, and a radius r = 3, as well



now, bear in mind the area of the cylinder, includes everything inside the cylinder, that means the cone along as well

so, if you subtract the area of the cone, from the area of the cylinder, you'd be making a "hole" in the cylinder, and what's leftover, is the shaded area.

Do you need with the x value for the minimum? its always between the two intercepts for a parabola