the volumes of two similar figures are 729 mm and 2744 mm if the surface area of the larger figure is 392 mm what is the surface area of the smaller figure

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26-04-2018
Mathematics

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the volumes of two similar figures are 729 mm and 2744 mm if the surface area of the larger figure is 392 mm what is the surface area of the smaller figure

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calculista calculista · Answer 1 · 2018-05-07T18:47:41+02:00

we know that
[volume of larger figure]=[scale]³*[volume of smaller figure]
scale=∛(volume of larger figure/volume of smaller figure)
scale=∛(2744/729)-----> 1.56

[surface area of the larger figure]=scale²*[surface area of the smaller figure]
[surface area of the smaller figure]=[surface area of the larger figure]/scale²
[surface area of the smaller figure]=[392]/1.56²----> 162 mm²

the answer is
the surface area of the smaller figure is 162 mm²