Answer:
[tex]V_{total}=293.50 cm^{3}[/tex]
Step-by-step explanation:
The composite solid is formed by a pyramid and a prism.
The formula of a pyramid is
[tex]V_{pyramid}=\frac{1}{3}Bh[/tex]
The formula of a rectangular prism is
[tex]V_{prism}=l\times w\times h[/tex].
The total volume is
[tex]V_{total}=V_{pyramid} +V_{prism}[/tex]
Where,
[tex]B=6.7cm\times 6.2 cm=41.51 cm^{2}[/tex]
[tex]V_{prism}=l\times w\times h=6.7cm \times 6.2cm \times 5.5cm=228.47cm^{3}[/tex]
Now, we need to find the height of the pyramid using the pythagorean theorem
[tex]5.8^{2}=(\frac{6.7}{2} )^{2}+h^{2} \\33.64=11.22+h^{2}\\h^{2} =33.64-11.22=22.42\\h=\sqrt{22.42} \approx 4.7[/tex]
So, the volume of the pyramid is
[tex]V_{pyramid}=\frac{1}{3}Bh=\frac{1}{3}(41.51)(4.7)=65.03cm^{3}[/tex]
Therefore, the volume of the composite figure is
[tex]V_{total}=65.03cm^{3}+228.47cm^{3}=293.50 cm^{3}[/tex]
