Answer:
176 in³
Step-by-step explanation:
Area is a 2-dimensional measure, so the scale factor for area of similar figures is the 2nd power of the linear scale factor. That is, the ratio of linear dimensions of the two figures is ...
smaller/larger = √(228/1425) = √(4/25) = 2/5 . . . . linear scale factor
Volume is a 3-dimensional measure, so the scale factor for volume of similar figures is the 3rd power of the linear scale factor. That is, the ratio of volumes of the two figures is ...
smaller/larger = (2/5)^3 = 8/125 . . . . . . . . volume scale factor
Multiplying this by the larger volume gives us the smaller volume:
(8/125)·(2750 in³) = 176 in³
so
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