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 - radius
H - height
We 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 - radius
Therefore 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]
