Answer: [tex]126\pi\ cm^3[/tex]
Step-by-step explanation:
In the given figure, we have a cylinder and 2 hemisphere with same diameter.
For Cylinder,
Radius = [tex]\frac{6}{2}=[/tex]3 inch
Height = 10 inch
Volume of cylinder is given by :-
[tex]\text{Volume of cylinder}=\pi r^2h\\\\\Rightarrow\ \text{Volume of cylinder}=\pi3^2(10)\\\\\Rightarrow\\text{Volume of cylinder}=90\pi\ cm^3[/tex]
For hemisphere,
Radius = 3 inch
Volume of hemisphere is given by :-
[tex]\text{Volume of hemisphere}=\frac{2}{3}\pi r^3\\\\\Rightarrow\ \text{Volume of hemisphere}=\frac{2}{3}\pi(3)^3\\\Rightarrow\text{Volume of hemisphere}=18\pi\ cm^3[/tex]
Now, Volume of 2 hemisphere = [tex]2\times18\pi=36\pi\ cm^3[/tex]
Volume of figure = Volume of cylinder+Volume of 2 hemisphere
[tex]=90\pi\ cm^3+36\pi\ cm^3=126\pi\ cm^3[/tex]
