the surface area of two similar figures are 16 in ^2 and 25 in ^2 if the volume of the larger figure is 500 in ^3 then what is the volume of the smaller figure?

256 in^3

Step-by-step explanation:

The ratio of linear dimensions is the square root of the ratio of areas, so the smaller figure has linear dimensions that are ...

√ ((16 in^2) / (25 in^2)) = 4/5

those of the larger figure.

The ratio of volumes is the cube of the ratio of linear dimensions, so the smaller figure will be (4/5) ^3 times the volume of the larger figure.

smaller figure volume = (4/5) ^3· (500 in^3) = (64/125) ·500 in^3 = 256 in^3