The scale factor of two similar solids is 6: 13. determine the ration of their corresponding areas and the volume of the larger solid if the volume of the smaller solid is 432 in^2. show all

The scale factor is given by:
 
 The relationship of the areas for this case is given by:
 
 Rewriting we have:
 
 The relation of volumes is:
 
 Where,
 V1: small solid volume
 V2: volume of the large solid
 Clearing V2 we have:
 
 Substituting values:
 
 
 The ratio of their corresponding areas is:
 36/169
 The volume of the larger solid is:
 4394 in ^ 3