Given,
The length of the whole shape is 13 inches.
The length of the cuboidal part is 8 inches.
The length of the pyramid part is 13- 8= 5 inches.
The side of the base of the both part is 6 inches.
The expression for the volume of the cuboidal part is,
[tex]V_1=l\times b\times h[/tex]
The expression for the volume of the pyramid part is,
[tex]V_2=a^2+2a\sqrt{a\frac{a^2}{4}+h^2}[/tex]
The volume of the whole shape is,
[tex]\begin{gathered} \text{Volume =V}_1+V_2 \\ \text{ =l}\times b\times h+a^2+2a\sqrt{\frac{a^2}{4}+h^2} \\ \text{ =8}\times6\times6+(6)^2+2\times6\sqrt[]{\frac{6^2}{4}+5^2} \\ \text{ =288}+36^{}+12\sqrt[]{\frac{36^{}}{4}+25} \\ \text{ =288}+36^{}+12\sqrt[]{9+25} \\ \text{ = 288}+36^{}+12\times5.83 \\ \text{ =393.971 inches}^3 \end{gathered}[/tex]
Hence, the volume of the shape is 393.971 inches cube.
