The surface areas of two similar solids are 200 m² and 1152 m². The volume of the larger one is 1728 m³. What is the volume of the smaller one?

Area scale factor is will be given by:

(area of smaller solid) / (area of larger solid)

=200/1152

=25/144

but

linear scale factor=√ (area scale factor)

=√ (25/144)

=5/12

to get the volume of the smaller figure we need volume scale factor

volume scale factor = (linear scale factor) ^3

= (5/12) ^3

=125/1728

thus the volume of the smaller figure will be:

125/1728*1728

=125 m³

Answer: 125 m³