Answer:[tex]\large\boxed{V=504\pi\ cm^3}[/tex]Step-by-step explanation:We have the cylinder and the half-sphere.The formula of a volume of a cylinder:[tex]V_c=\pi r^2H[/tex]r - radiusH - heightWe have r = 6cm and H = 10cm.Substitute:[tex]V_c=\pi(6^2)(10)=\pi(36)(10)=360\pi\ cm^3[/tex]The formula of a volume of a sphere:[tex]V_s=\dfrac{4}{3}\pi R^3[/tex]R - radiusTherefore the formula of a volume of a half-sphere is:[tex]V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3[/tex]We have R = 6cm. Substitute:[tex]V_{hs}=\dfrac{2}{3}\pi(6^3)=\dfrac{2}{3}\pi(216)=\dfrac{2}{1}\pi(72)=144\pi\ cm^3[/tex]The volume of the given shape:[tex]V=V_c+V_{hs}[/tex]Substitute:[tex]V=360\pi+144\pi=504\pi\ cm^3[/tex]