Answer: The volume of the composite figure is 140 in³.
Step-by-step explanation: We are given to find the volume of the composite figure shown in the diagram.
The figure is composed of two geometrical figures :
(A) A cuboid of dimension 3 in. by 4 in. by 7 in.
So, the volume of the cuboid will be
[tex]V_c=3\times4\times7=84~\textup{in}^3.[/tex]
(B) A rectangular pyramid of height 8 in. and base of dimension 3 in. by 7 in.
So, the volume of the pyramid will be
[tex]V_p=\dfrac{8\times3\times7}{3}=56~\textup{in}^3.[/tex]
Therefore, the volume of both the cuboid and pyramid is
[tex]V=V_c+V_p=84+56=140~\textup{in}^3.[/tex]
Thus, the required volume of the composite figure is 140 in³.
