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Which of the following volumes represent a perfect cube? Check all that apply.

- 0.1 in³
- 0.4 in³
- 8 in³
- 12 in³
- 25 in³
- 27 in³
- 64 in³

Answer :

To determine which volumes are perfect cubes, you want to identify the numbers that can be expressed as the cube of an integer. Let's check each given volume:

1. 0.1 in.³: The cube root of 0.1 is a small, non-integer number. Therefore, 0.1 is not a perfect cube.

2. 0.4 in.³: The cube root of 0.4 also results in a non-integer number. Hence, 0.4 is not a perfect cube.

3. 8 in.³: The cube root of 8 is 2, since 2 × 2 × 2 = 8. Thus, 8 is a perfect cube.

4. 12 in.³: The cube root of 12 is not an integer since it falls between 2 and 3. Therefore, 12 is not a perfect cube.

5. 25 in.³: The cube root of 25 is a non-integer because it's between 2 and 3. So, 25 is not a perfect cube.

6. 27 in.³: The cube root of 27 is 3, since 3 × 3 × 3 = 27. So, 27 is a perfect cube.

7. 64 in.³: The cube root of 64 is 4, since 4 × 4 × 4 = 64. Thus, 64 is a perfect cube.

In conclusion, the volumes that represent perfect cubes are 8 in.³, 27 in.³, and 64 in.³.

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