Answer:
112 in³
Step-by-step explanation:
The pedestal is made up of two rectangular prisms.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Volume of a rectangular prism}\\\\$V=w\cdot l\cdot h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base.\\\phantom{ww}$\bullet$ $h$ is the height of the prism.\\\end{minipage}}[/tex]
The dimensions of the largest rectangular prism are:
Therefore, the volume of the largest rectangular prism is:
[tex]\begin{aligned}\implies V&=2 \cdot 9 \cdot 4\\&=18 \cdot 4\\&=72\;\rm in^3\end{aligned}[/tex]
The dimensions of the smaller rectangular prism are:
- w = 2 in
- l = 9 - 2 - 2 = 5 in
- h = 4 in
Therefore, the volume of the smaller rectangular prism is:
[tex]\begin{aligned}\implies V&=2 \cdot 5 \cdot 4\\&=10\cdot 4\\&=40\;\rm in^3\end{aligned}[/tex]
The volume of the pedestal is the sum of the volumes of the largest and smaller rectangular prisms:
[tex]\implies V=72+40=112\; \rm in^3[/tex]
Therefore, the volume of the pedestal is 112 in³.
