Question

Which of the following volumes represent a perfect cube? Check all that apply.
1 in.3
4 in.3
8 in.3
12 in.3
25 in.3
27 in.3
64 in.3

Answer 1

To determine which volumes represent a perfect cube, we need to check if the volume is the cube of a whole number.

A volume \( V \) is a perfect cube if there exists an integer \( n \) such that \( V = n^3 \).

Let's evaluate each option:

1. \( 1 \, \text{in}^3 = 1^3 \) (perfect cube)
2. \( 4 \, \text{in}^3 \) (not a perfect cube)
3. \( 8 \, \text{in}^3 = 2^3 \) (perfect cube)
4. \( 12 \, \text{in}^3 \) (not a perfect cube)
5. \( 25 \, \text{in}^3 \) (not a perfect cube)
6. \( 27 \, \text{in}^3 = 3^3 \) (perfect cube)
7. \( 64 \, \text{in}^3 = 4^3 \) (perfect cube)

The volumes that represent a perfect cube are:
- \( 1 \, \text{in}^3 \)
- \( 8 \, \text{in}^3 \)
- \( 27 \, \text{in}^3 \)
- \( 64 \, \text{in}^3 \)

Thus, the answers are:
- \( 1 \, \text{in}^3 \)
- \( 8 \, \text{in}^3 \)
- \( 27 \, \text{in}^3 \)
- \( 64 \, \text{in}^3 \)