The edge of a cubical box is doubled. The new volume is how many times the old volume?

Class 8Cubes and Cube RootsCubes and Roots

Step-by-Step Solution

If the edge grows from a to

2 a

, the volume grows from

a^{3}

(2 a)^{3} = 8 a^{3}

— a factor of 8. Answering 2 times doubles only one dimension; doubling the edge doubles all three, so the factor is

2 \times 2 \times 2

Answer: C) 8 times

Both are repeated multiplication, but with key differences:

- A square is non-negative:

(- 5)^{2} = + 25

.
- A cube **keeps the sign**:

(- 5)^{3} = - 125

. (Three negatives stay odd → still negative.)
- Squares grow more slowly than cubes:

5^{2} = 25

5^{3} = 125. -

For square roots, only positive results (by convention). For cube roots, the sign matches the input: ∛

(- 27) = - 3

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