Question

The two cubes are similar in shape. Compare the volume of the two and determine the scale factor from the smaller cube to the larger cube. Enter your response as a fraction. The scale factor from the smaller cube to the larger cube is _. One cube is V=512 m^3 and the other cube is V=1728 m^3.

Answer 1

Volume ratio = 1728:512 = 1728/512 = 27/8. For cubes, linear scale factor k satisfies k^3 = 27/8, so k = (27/8)^(1/3) = 3/2.

The scale factor from the smaller cube to the larger cube is 3/2.