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To find the volume of the smaller solid, we can use the concept of similarity between the two solids.
Since the two solids are similar, their volumes will be proportional to the cubes of their corresponding dimensions.
Let the volume of the smaller solid be x yd^3.
We can set up a proportion based on the surface areas of the two solids:
(384 / 1057)^2 = x / 1795
(0.3630)^2 = x / 1795
0.1317 = x / 1795
x = 0.1317 * 1795
x ≈ 236.48
Therefore, the volume of the smaller solid is approximately 236.48 yd^3.