Question

What is the scale factor of a cube with a volume of 343 m^3 to a cube with a volume of 5832 m^3>

A. 324:49

B. 49:324

C. 18:7

D. 7:18

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the scale factor, we need to take the cube root of the ratio of the volumes.

Volume of first cube: 343 m^3
Volume of second cube: 5832 m^3

Scale factor = (5832/343)^(1/3)
Scale factor = (17)^(1/3)
Scale factor = ³√17

So the scale factor is not a whole number. We can simplify it to a ratio by taking the cube of 17.

Approximating the cube root of 17 to be between 2 and 3, let's calculate with 2 and 3:

2^3 = 8
3^3 = 27

The cube root of 17 would be between 2 and 3, closer to 2. Therefore, the scale factor is approximately 2:1.

Since none of the answer choices is a ratio of 2:1, there may have been a mistake in the calculations or problem setup. It's possible that the answer choices provided are incorrect or there is an error in the question.