Question

The surface areas of two similar figures are 4 in2 and 9 in2. If the volume of the larger figure is 216 in3, what is the volume of the smaller figure?

Answer 1

We know that
surface area smaller figure=scale factor²*surface area larger figure
scale factor=√[surface area smaller figure/surface area larger figure]
scale factor=√[4/9]-----> scale factor=2/3
so
volume smaller figure=scale factor³*volume larger figure
volume smaller figure=(2/3)³*216----> (8/27)*216----> 64 in³

the answer is
the volume of the smaller figure is 64 in³