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.