Answer:
113.1 [tex]cm^{3}[/tex]
Step-by-step explanation:
The equation to find the volume of a cylinder is:
[tex]V = \pi r^{2} h[/tex]
V = volume
r = radius
h = height
The radius of the cylinder is 3 in, and the height of the cylinder is 2 in. Plug these into the equation:
[tex]V = \pi (3)^{2} (2)[/tex]
Solve (use calculator):
V = [tex]18\pi[/tex] or 56.55 [tex]cm^{3}[/tex]
To find the volume of the half sphere use this equation:
[tex]V = \frac{1}{2}(\frac{4}{3} \pi r^{3} )[/tex]
The radius of the circle is 3 in, plug this into the equation:
[tex]V=\frac{1}{2} (\frac{4}{3} \pi (3^{3}))[/tex]
Solve (use calculator):
V = [tex]18\pi[/tex] or 56.55 [tex]cm^{3}[/tex]
To find the volume of the entire shape just add the separate volumes together:
V( of cylinder) + V( of sphere) = Total volume
[tex]56.55 cm^{3}+56.55 cm^{3}= 113.1 cm^{3}[/tex]
Or, you could rewrite this as 36[tex]\pi[/tex]
So, the answer is that the volume of the composite solid is 113.1 [tex]cm^{3}[/tex]
