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