Question

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. Please show all work!!

Answer 1

I first begin by dividing 13 by 6 to get 2.16666666667. I then multiple that number by 432 in^2 to get the answer : 936 in^2 for the larger solid. 

Answer 2

The scale factor is given by:
 $k = 6/13$
 The relationship of the areas for this case is given by:
 $k ^ 2 = (6/13) ^ 2$
 Rewriting we have:
 $k ^ 2 = (6/13) ^ 2 k ^ 2 = 36/169$
 The relation of volumes is:
 $k ^ 3 = V1 / V2$
 Where,
 V1: small solid volume
 V2: volume of the large solid
 Clearing V2 we have:
 $V2 = V1 / k ^ 3$
 Substituting values:
 $V2 = 432 / (6/13) ^ 3 V2 = 4394 in ^ 3$
 Answer:
 The ratio of their corresponding areas is:
 36/169
 The volume of the larger solid is:
 4394 in ^ 3