Answer:
[tex]6.7 \, \textsf{ft}^3[/tex]
Step-by-step explanation:
To find the volume of the composite figure, which is the difference between the volume of the cuboid and the pyramid, we need to calculate the volume of each shape separately and then subtract the volume of the pyramid from the volume of the cuboid.
Volume of the Cuboid:
[tex] V_{\textsf{cuboid}} = \textsf{Length} \times \textsf{Width} \times \textsf{Height} [/tex]
[tex] V_{\textsf{cuboid}} = 1 \, \textsf{ft} \times 1 \, \textsf{ft} \times 8 \, \textsf{ft} [/tex]
[tex] V_{\textsf{cuboid}} = 8 \, \textsf{ft}^3 [/tex]
Volume of the Pyramid:
The formula for the volume of a pyramid is given by:
[tex] V_{\textsf{pyramid}} = \dfrac{1}{3} \times \textsf{Base Area} \times \textsf{Height} [/tex]
The base area of the pyramid is [tex]1 \, \textsf{ft} \times 1 \, \textsf{ft} = 1 \, \textsf{ft}^2[/tex].
[tex] V_{\textsf{pyramid}} = \dfrac{1}{3} \times 1 \, \textsf{ft}^2 \times 3.9 \, \textsf{ft} [/tex]
[tex] V_{\textsf{pyramid}} = 1.3 \, \textsf{ft}^3 [/tex]
Volume of the Composite Figure:
[tex] V_{\textsf{composite}} = V_{\textsf{cuboid}} - V_{\textsf{pyramid}} [/tex]
[tex] V_{\textsf{composite}} = 8 \, \textsf{ft}^3 - 1.3 \, \textsf{ft}^3 [/tex]
[tex] V_{\textsf{composite}} \approx 6.7 \, \textsf{ft}^3 [/tex]
So, the volume of the composite figure is approximately [tex]6.7 \, \textsf{ft}^3[/tex].
