Solution:
Given the figure below:
To find the volume of the shaded solid, we subtract the volume of the cylinder from the volume of the entire cuboid.
step 1: Evaluate the volume of the cuboid.
The volume of the cuboid is expressed as
[tex]\begin{gathered} Volume=length\times width\times height \\ thus,\text{ we have} \\ V_{cuboid}=24\times6\times6 \\ =864\text{ }m^3 \end{gathered}[/tex]
step 2: Evaluate the volume of the cylinder.
The volume of a cylinder is expressed as
[tex]\begin{gathered} Volume=\pi\times(radius)^2\times height \\ thus,\text{ we have} \\ V_{cylinder}=3.14\times(\frac{6}{2})^2\times24 \\ =678.24\text{ }m^3 \end{gathered}[/tex]
step 3: Evaluate the volume of the shaded solid.
Thus, we have
[tex]\begin{gathered} V_{shaded\text{ solid}}=V_{cylinder}-V_{cuboid} \\ =864-678.24 \\ =185.76 \end{gathered}[/tex]
Hence, to 2 decimal places, the volume of the solid figure is evaluated to be
[tex]185.76\text{ m}^3[/tex]
