The surface areas of two similar solids are 169 m2 and 81 m2. The volume of the larger solid is 124.92 m3. Which proportion correctly shows how to solve for the volume of the smaller solid, x?

A:13/9 = 124.92/x

B:169/81 = 124.92/x

C:13^3/9^3 = 124.92/x

D:169^3/81^3 = 124.92/x

C

Step-by-step explanation:

Given 2 similar solids whose

ratio of sides = a : b, then

ratio of areas = a^2 : b^2 and

ratio of volumes = a^3 : b^3

Here the area ratio = 169 : 81, thus

side ratio = sqrt{169} : sqrt{81} = 13 : 9

Hence the volume ratio = 13^3 : 9^3

Using proportion then

frac{13^3}{9^3} = frac{124.92}{x} → C

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step-by-step explanation: