Answer:
The first step is to find the volume of the two hemispheres.
Step-by-step explanation:
[tex]\boxed{volume \: of \: sphere = \frac{4}{3} \pi {r}^{3} }[/tex]
Since the 2 hemispheres have the same radius, we can simply find the volume of a sphere.
Volume of sphere
[tex] = \frac{4}{3}( \pi)( {12}^{3} )[/tex]
[tex] = 2304\pi \: in^{3} [/tex]
Volume of solid
= volume of cylinder -volume of 2 hemispheres
Let's find the volume of the cylinder.
[tex]\boxed{voume \: of \: cylinder = \pi {r}^{2}h }[/tex]
Volume of cylinder
[tex] = \pi( {12}^{2} )(24)[/tex]
[tex] = 3456\pi \: in^{3} [/tex]
Thus, volume of solid
[tex] = 3456\pi - 2304\pi[/tex]
[tex] = 1152\pi[/tex]
[tex] = 1152(3.14)[/tex]
[tex] = 3617.28 \: in^{3} [/tex]
