Question

the volume of solid A is 28m3 and the volume of solid B is 1,792m3. If the solids are similar, what is the ratio of the surface area of solid A to the surface area of solid B

Answer 1

If k is the scale factor between the dimensions of the similar solids, the areas are related by k² and the volumes are related by k³. That is
$\ \ \dfrac{V_{a}}{V_{b}}=k^{3}$
$\ \ k=(\dfrac{V_{a}}{V_{b}})^{\frac{1}{3}}$

The areas are related by k², so
$\ \ \dfrac{A_{a}}{A_{b}}=k^{2} = (\dfrac{V_{a}}{V_{b}})^{\frac{2}{3}}$
$\ \ \dfrac{A_{a}}{A_{b}} = (\dfrac{28\ m^{3}}{1792\ m^{3}})^{\frac{2}{3}}=(4^{-3})^{\frac{2}{3}}$
$\ \ =4^{-2}=\dfrac{1}{16}$

The ratio of the surface area of solid A to that of solid B is ...
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