You can identify that the whole solid is formed by a cylinder and a hemisphere.
The formula to calculate the volume of a cylinder is:
[tex]V_c=\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cylinder.
The formula to calculate the volume of a hemisphere is:
[tex]V_h=\frac{2}{3}\pi r^3[/tex]
Where "r" is the radius.
Knowing these formulas, you can set up the following equation to calculate the total volume of the solid. Remember to use:
[tex]\pi\approx3.14[/tex]
Then:
[tex]V_t=(3.14\cdot r^2\cdot h)+(\frac{2}{3}\cdot3.14\cdot r^3)[/tex]
You know that:
[tex]\begin{gathered} r=8ft \\ h=9ft \end{gathered}[/tex]
Therefore, you can substitute values into the equation and evaluate:
[tex]\begin{gathered} V_t=(3.14)(8ft)^2(9ft)+(\frac{2}{3})(3.14)(8ft)^3 \\ \\ V_t=1808.64ft^3+1071.78667ft^3 \end{gathered}[/tex][tex]V_t\approx2880.427ft^3[/tex]
Therefore, the answer is:
[tex]2880.427ft^3[/tex]
