Answer:
[tex] 8600.5 \, \textsf{cm} ^3 [/tex]
Step-by-step explanation:
To find the volume of the composite solid, which is a combination of a cuboid and a semi-cylinder, we can calculate the volumes of each component separately and then add them together.
Cuboid Volume:
The volume [tex]V_\textsf{cuboid}[/tex] of a cuboid is given by the formula:
[tex] V_\textsf{cuboid} = \textsf{length} \times \textsf{width} \times \textsf{height} [/tex]
Substituting the given values:
[tex] V_\textsf{cuboid} = 24.8 \, \textsf{cm} \times 9 \, \textsf{cm} \times 35 \, \textsf{cm} [/tex]
[tex] V_\textsf{cuboid} = 7812\, \textsf{cm} ^3[/tex]
Semi-Cylinder Volume:
The volume [tex]V_\textsf{semi-cylinder}[/tex] of a semi-cylinder is given by half the volume of a full cylinder:
[tex] V_\textsf{semi-cylinder} = \dfrac{1}{2} \times \pi \times \textsf{radius}^2 \times \textsf{length} [/tex]
Given that the diameter is 9 cm, the radius is half of the diameter, so [tex] \textsf{radius} = \dfrac{9}{2} [/tex] cm.
Substituting the values:
[tex] V_\textsf{semi-cylinder} = \dfrac{1}{2} \times 3.14 \times \left( \dfrac{9}{2} \right)^2 \times 24.8 [/tex]
[tex] V_\textsf{semi-cylinder} = 788.454\, \textsf{cm} ^3[/tex]
Now, we can add the volumes of the cuboid and the semi-cylinder to get the total volume:
[tex] \textsf{Total Volume} = V_\textsf{cuboid} + V_\textsf{semi-cylinder} [/tex]
[tex] \textsf{Total Volume} = 7812\, \textsf{cm} ^3 + 788.454\, \textsf{cm} ^3[/tex]
[tex] \textsf{Total Volume} = 8600.454 \, \textsf{cm} ^3 [/tex]
[tex] \textsf{Total Volume} = 8600.5 \, \textsf{cm} ^3 \textsf{(in nearest tenth)}[/tex]
So, the volume of the composite solid is:
[tex] 8600.5 \, \textsf{cm} ^3 [/tex]
