The edge of a cube is doubled then the percentage increase in the volume of cube is

Options

A. `100%`
B. `500%`
C. `300%`
D. `700%`

Answer

To solve the problem of finding the percentage increase in the volume of a cube when its edge is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Edge of the Cube**:
Let the edge of the cube be \( a \) units.

2. **Calculate the Original Volume**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
So, the original volume of the cube is \( a^3 \).

3. **Double the Edge Length**:
When the edge of the cube is doubled, the new edge length becomes \( 2a \).

4. **Calculate the New Volume**:
The new volume \( V' \) of the cube with the doubled edge length is:
\[ V' = (2a)^3 = 2^3 \cdot a^3 = 8a^3 \]

5. **Find the Increase in Volume**:
The increase in volume can be calculated as:
\[ \text{Increase in Volume} = V' - V = 8a^3 - a^3 = 7a^3 \]

6. **Calculate the Percentage Increase**:
The percentage increase in volume is given by the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Volume}}{\text{Original Volume}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{7a^3}{a^3} \right) \times 100 = 7 \times 100 = 700\% \]

### Final Answer:
The percentage increase in the volume of the cube when the edge is doubled is **700%**.