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Colt1911 [192]
3 years ago
6

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
Mathematics
1 answer:
Maslowich3 years ago
6 0
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 ...
  1/16
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