What will be the change in the volume of a cube when its side becomes 10 times the original side?

Options

A. Volume becomes 1000 times.
B. Volume becomes 10 times.
C. Volume becomes 100 times.
D. Volume becomes `1/1000` times

Answer

To solve the problem, we need to determine how the volume of a cube changes when its side length is increased to 10 times its original length.

### Step-by-Step Solution:

1. **Understand the Volume Formula**:
The volume \( V \) of a cube with side length \( a \) is given by the formula:
\[ V = a^3 \]

2. **Calculate the Original Volume**:
Let the original side length of the cube be \( a \). Therefore, the original volume \( V_{\text{original}} \) is:
\[ V_{\text{original}} = a^3 \]

3. **Determine the New Side Length**:
If the side length becomes 10 times the original side, the new side length \( a_{\text{new}} \) is:
\[ a_{\text{new}} = 10a \]

4. **Calculate the New Volume**:
Using the new side length, the new volume \( V_{\text{new}} \) can be calculated as:
\[ V_{\text{new}} = (a_{\text{new}})^3 = (10a)^3 \]
Simplifying this gives:
\[ V_{\text{new}} = 10^3 \cdot a^3 = 1000a^3 \]

5. **Determine the Change in Volume**:
To find the change in volume, we compare the new volume to the original volume:
\[ \text{Change in Volume} = V_{\text{new}} - V_{\text{original}} = 1000a^3 - a^3 \]
This simplifies to:
\[ \text{Change in Volume} = 999a^3 \]

6. **Determine the Factor of Change**:
The factor by which the volume has increased is:
\[ \text{Factor of Change} = \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{1000a^3}{a^3} = 1000 \]

### Final Answer:
The volume of the cube increases by a factor of 1000 when its side length is increased to 10 times the original side length.

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