Answer:
[tex] \textsf{Volume} = 23499.6 \, \textsf{cm} ^3[/tex]
Step-by-step explanation:
To find the volume of the composite figure, which consists of a cuboid and a cylinder, subtract the volume of the cylinder from the volume of the cuboid.
Volume of Cuboid ([tex]V_{\textsf{cuboid}})[/tex]:
[tex] V_{\textsf{cuboid}} = \textsf{length} \times \textsf{width} \times \textsf{height} [/tex]
[tex] V_{\textsf{cuboid}} = 48 \, \textsf{cm} \times 28 \, \textsf{cm} \times 18 \, \textsf{cm} [/tex]
[tex] V_{\textsf{cuboid}} = 24192 \, \textsf{cm}^3 [/tex]
Volume of Cylinder ([tex]V_{\textsf{cylinder}})[/tex]:
[tex] V_{\textsf{cylinder}} = \pi r^2 \times \textsf{height} [/tex]
Given the diameter [tex]d = 7 \, \textsf{cm}[/tex], the radius [tex]r = \dfrac{d}{2} = \dfrac{7}{2} \, \textsf{cm}[/tex].
[tex] V_{\textsf{cylinder}} = 3.14 \times \left(\dfrac{7}{2}\right)^2 \times 18 \, \textsf{cm} [/tex]
[tex] V_{\textsf{cylinder}} = 692.37 \, \textsf{cm} ^3 [/tex]
Volume of Composite Figure:
[tex] \textsf{Volume} = V_{\textsf{cuboid}} - V_{\textsf{cylinder}} [/tex]
[tex] \textsf{Volume} = 24192 \, \textsf{cm}^3 - 692.37 \, \textsf{cm} ^3 [/tex]
[tex] \textsf{Volume} = 23499.63 \, \textsf{cm} ^3[/tex]
[tex] \textsf{Volume} = 23499.6 \, \textsf{cm} ^3 \textsf{ ( in nearest tenth)}[/tex]
So, the volume of the composite figure is:
[tex] \textsf{Volume} = 23499.6 \, \textsf{cm} ^3 [/tex]
