Answer:
93.75 cm^3
Explanation:
Given the following;
Base area of the prism = 8 cm^2
Height of the prism = 6cm
Scale factor = 5/4
Let's go ahead and determine the volume of the original prism before the dilation;
[tex]\text{Volume of original prism = Base area x Height }=8\cdot6=48cm^3[/tex]So the volume of the original prism before dilation is 48cm^3
Let's go ahead and determine the volume of the dilated prism as seen below;
[tex]\begin{gathered} \text{Volume of dilated prism }=\text{Volume of original prism x (Scale factor)\textasciicircum{}3} \\ =48\cdot(\frac{5}{4})^3 \\ =48\cdot\frac{125}{64} \\ =93.75cm^3 \end{gathered}[/tex]So the volume of the dilated prism is 93.75 cm^3
