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 [tex]\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\implies V=\pi 3^3\cdot 9\implies V=243\pi [/tex]
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
[tex]\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{\pi 3^3\cdot 9}{3}\implies V=\cfrac{243\pi }{3}[/tex]
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.
