Question

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?

Answer 1

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