What is the scale factor of a cube with a volume of 343 m3 to a cube with a volume of 5,832 m3? (1 point) Responses 324:49 324:49 49:324 49:324 18:7 18:7 7:18
To compare the scale factors of two cubes based on their volumes, you first need to compute the cube roots of their volumes to find the lengths of their sides (since the volume of a cube is the cube of its side length).
For the first cube with a volume of 343 m³:
Volume = side length³
343 m³ = side length³
side length = ³√343 = 7 m (since 7 × 7 × 7 = 343)
For the second cube with a volume of 5,832 m³:
Volume = side length³
5,832 m³ = side length³
side length = ³√5,832 ≈ 18 m (since 18 × 18 × 18 = 5,832)
Now, to find the scale factor from the smaller cube to the larger cube, you divide the side length of the larger cube by the side length of the smaller cube:
Scale factor = side length of larger cube / side length of smaller cube
Scale factor ≈ 18 m / 7 m = 18:7
Therefore, the scale factor of a cube with a volume of 343 m³ to a cube with a volume of 5,832 m³ is 18:7.