Given the volume of two cubes, find the scale factor.

6) V = 343 in3 and V = 729 in3

7) V = 1331 ft3 and V = 125 ft3

The volume of similar solids are proportional to the cube of the linear measurements.

So to find the scale factor, compare the cube-roots of the volumes.

To find the scale factor between two cubes, we can use the formula:

scale factor = cube root (V2 / V1)

Let's plug in the values for each scenario:

6) V1 = 343 in^3 and V2 = 729 in^3

First, calculate the cube root of V2 / V1:

scale factor = cube root (729 in^3 / 343 in^3) ≈ 1.6

Therefore, the scale factor for this scenario is approximately 1.6.

7) V1 = 1331 ft^3 and V2 = 125 ft^3

Similarly, calculate the cube root of V2 / V1:

scale factor = cube root (125 ft^3 / 1331 ft^3) ≈ 0.5

So, the scale factor for this scenario is approximately 0.5.