EXPLANATION:
Given;
We are given a half sphere placed inside a cylinder.
The dimensions of both solid shapes are as follows;
[tex]\begin{gathered} Hemi-sphere: \\ radius=3ft \end{gathered}[/tex][tex]\begin{gathered} Cylinder: \\ radius=3ft \\ height=5ft \end{gathered}[/tex]
The volume of a hemisphere is given by the formula;
[tex]Volume=\frac{2}{3}\pi r^3[/tex]
We shall substitute the values given and we'll have;
[tex]Volume=\frac{2}{3}\times\pi\times3^3[/tex][tex]Volume=\frac{2}{3}\times\pi\times27[/tex][tex]Volume=18\pi ft^3[/tex]
The volume of a cylinder is given by the formula;
[tex]Volume=\pi r^2h[/tex]
We now have;
[tex]Volume=\pi\times3^2\times5[/tex][tex]Volume=45\pi ft^3[/tex]
Therefore, the volume of the composite figure is;
[tex]Volume=hemisphere+cylinder[/tex][tex]Volume=18\pi+45\pi[/tex][tex]Volume=63\pi ft^3[/tex]
ANSWER:
[tex]Volume\text{ }of\text{ }the\text{ }composite\text{ }figure=63\pi ft^3[/tex]
