Answer:
[tex]\large\boxed{V=\dfrac{1,421\pi}{3}\ cm^3}[/tex]
Step-by-step explanation:
We have the cone and the half-sphere.
The formula of a volume of a cone:
[tex]V_c=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have r = 7cm and H = (22-7)cm=15cm. Substitute:
[tex]V_c=\dfrac{1}{3}\pi(7^2)(15)=\dfrac{1}{3}\pi(49)(15)=\dfrac{735\pi}{3}\ 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:
[tex]V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3[/tex]
We have R = 7cm. Substitute:
[tex]V_{hs}=\dfrac{2}{3}\pi(7^3)=\dfrac{2}{3}\pi(343)=\dfrac{686\pi}{3}\ cm^3[/tex]
The volume of the given shape:
[tex]V=V_c+V_{hs}[/tex]
Substitute:
[tex]V=\dfrac{735\pi}{3}+\dfrac{686\pi}{3}=\dfrac{1,421\pi}{3}\ cm^3[/tex]
