Question

The scale factor of two similar solids is 6:13 determine the ratio of their corresponding areas and the volume of the larger solid if the volume of the smaller solid is 432in2

Answer 1

The ratio of the corresponding areas of two similar solids with a scale factor of 6:13 is 36:169. The volume of the larger solid is 2197in^3.

Step-by-step explanation:

The scale factor is given as 6:13, which means that for every 6 units of the smaller solid, there are 13 units of the larger solid. To find the ratio of their corresponding areas, we square the scale factor. So it becomes 6^2:13^2 = 36:169. Therefore, the ratio of their corresponding areas is 36:169.

To determine the volume of the larger solid, we cube the scale factor. So it becomes 6^3:13^3 = 216:2197. Therefore, the volume of the larger solid is 2197in^3.

Answer 2

1. If the scale factor is k=6:13, then the ratio of their corresponding area is
`k^(2)=6^(2) :13^(2) =36:169`;
2.
`(V_(small\ solid))/(V_(big\ solid)) =k^3= (6^(3))/(13^(3)) = (216)/(2197)`.