so you have a small sphere(core) inside a larger sphere, we'll simply get the volume of the larger sphere, and then get the volume of the smaller one, and subtract the smaller's volume from the larger's, what's leftover, is the outer part to the core,
a radius is half of a diameter, thus the larger's radius is 9, and the smaller's radius is 4.5,
[tex]\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\\\\
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\cfrac{4\pi (9)^3}{3}~~~~-~~~~\cfrac{4\pi (4.5)^3}{3}\implies \cfrac{2916\pi -364.5\pi }{3}\implies \cfrac{2551.5\pi }{3}[/tex]
