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

Scale is a one-to-one measure, which can be used as a perimeter measure if needed.  Area, then, takes this one-to-one and squares it, because area is a squared measure (whereas perimeter is a single unit measure).  Volume is a cubed measure.  To find the ratio of the areas, we will take the one-to-one ratio and square it: .  To find the volume ratio, take the same one-to-one and cube it: .  Now we can set up a proportion using the smaller volume.  The smaller of the values for the volume is on top and the larger is on bottom: .  Cross-multiply to get 216x=949104.  Solving for x will give us the larger volume: x = 4394