Respuesta :
For similar solids, the ratios of the two sides (R), two areas (A) and two volumes (V) are
[tex]\frac{R_1}{R_2}\Rightarrow\text{Ratio of sides}[/tex][tex]\frac{A_1}{A_2}=\frac{(R^{}_1)^2}{(R_2)^2}\Rightarrow\text{Ratio of surface areas}[/tex][tex]\begin{gathered} \frac{V_1}{V_2}=\frac{(R_1)^3}{(R_2)^3} \\ 3\sqrt[]{\frac{V_1}{V_2}}=\frac{R_1}{R_2} \end{gathered}[/tex]Therefore, we can relate the volumes as follows:
[tex]\frac{V_1}{V_2_{}}=\frac{28}{1792}=\frac{1}{64}[/tex]The ratio of the sides is given as
[tex]\frac{R_1}{R_2}=3\sqrt[]{\frac{1}{64}}=\frac{1}{4}[/tex]Therefore, the ratio of the surface areas is given as
[tex]\frac{A_1}{A_2}=\frac{1^2}{4^2}=\frac{1}{16}[/tex]Therefore, the ratio is 1:16.
