The dimensions of prism A is 5 inches by 5 inches by 6 inches
And dimensions of prism B is 2 inches by 4 inches by 6 inches.
By checking the dimensions we can predict that the prism with the least surface area to volume ratio is prism A.
The correct option is A.
The volume of prism A is determined as
[tex]\begin{gathered} V=5\times5\times6=150in^3 \\ \end{gathered}[/tex]
The surface area of prism A is
[tex]S=2(5\times5+5\times6+6\times5)=2(25+30+30)[/tex]
[tex]S=2\times85=170in^2[/tex]
The actual ratio of surface area to volume for this prism after calculating is
[tex]\frac{170in^2}{150in^3}=\frac{17in^2}{15in^3}=1.13[/tex]
The correct option is D.
