Explanation
Step 1
the volume of a square pyramid is given by
[tex]Volume=\frac{side^2\cdot heigth}{3}[/tex]we are told that:
volume of the entire pyramid is
[tex]\begin{gathered} 96cm^3=\frac{side_1^2\cdot heigth_1}{3} \\ 96cm^3=\frac{6^2\cdot8}{3} \\ 96cm^3=96cm^3 \end{gathered}[/tex]Step 2
now, the measures are reducted by a scale factor of 0.5,it means.
[tex]\begin{gathered} \text{side}_2=0.5\cdot side_1=0.5\cdot6=3 \\ \text{height}_2=0.5\cdot height_1=0.5\cdot8=4 \end{gathered}[/tex]now, replace
the volume of the small pyramid would be.
[tex]\begin{gathered} Volume=\frac{side^2\cdot heigth}{3} \\ Volume=\frac{3^2\cdot4}{3}=3\cdot4=12 \\ Volume=12cm^3 \end{gathered}[/tex]I hope this helps you
