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The volumes of two similar figures are 27 mm^3 and 1331 mm^3. If the surface area of the smaller figure is 18 mm^2, what is the surface area of the larger figure?

Answer :

volumes are in ratio 27 : 1331
so ratio od individual lengths  = cube roots  = 3 : 11
and surface areas will be in the ratio  3^2 : 11^2 = 9:121

so surface area of the larger figure  is  121 * 18  / 9  =  242 mm^2

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